diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4fcd5acb81..ae4616a2d4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,7 @@
 
 ## Features
 
+- Added new parameters `"f{pref]Initial inner SEI on cracks thickness [m]"` and `"f{pref]Initial outer SEI on cracks thickness [m]"`, instead of hardcoding these to `L_inner_0 / 10000` and `L_outer_0 / 10000`. ([#4168](https://github.com/pybamm-team/PyBaMM/pull/4168))
 - Added `pybamm.DataLoader` class to fetch data files from [pybamm-data](https://github.com/pybamm-team/pybamm-data/releases/tag/v1.0.0) and store it under local cache. ([#4098](https://github.com/pybamm-team/PyBaMM/pull/4098))
 - Transport efficiency submodel has new options from the literature relating to different tortuosity factor models and also a new option called "tortuosity factor" for specifying the value or function directly as parameters ([#3437](https://github.com/pybamm-team/PyBaMM/pull/3437))
 - Added `plot_thermal_components` to plot the contributions to the total heat generation in a battery ([#4021](https://github.com/pybamm-team/PyBaMM/pull/4021))
diff --git a/pybamm/input/parameters/lithium_ion/Ai2020.py b/pybamm/input/parameters/lithium_ion/Ai2020.py
index 2bf1eeecdd..b45c04fa7f 100644
--- a/pybamm/input/parameters/lithium_ion/Ai2020.py
+++ b/pybamm/input/parameters/lithium_ion/Ai2020.py
@@ -549,6 +549,8 @@ def get_parameter_values():
         "Lithium interstitial reference concentration [mol.m-3]": 15.0,
         "Initial inner SEI thickness [m]": 2.5e-09,
         "Initial outer SEI thickness [m]": 2.5e-09,
+        "Initial inner SEI on cracks thickness [m]": 2.5e-13,  # avoid division by zero
+        "Initial outer SEI on cracks thickness [m]": 2.5e-13,  # avoid division by zero
         "EC initial concentration in electrolyte [mol.m-3]": 4541.0,
         "EC diffusivity [m2.s-1]": 2e-18,
         "SEI kinetic rate constant [m.s-1]": 1e-12,
diff --git a/pybamm/input/parameters/lithium_ion/OKane2022.py b/pybamm/input/parameters/lithium_ion/OKane2022.py
index d3e43c1e90..b1e852dbdf 100644
--- a/pybamm/input/parameters/lithium_ion/OKane2022.py
+++ b/pybamm/input/parameters/lithium_ion/OKane2022.py
@@ -536,6 +536,8 @@ def get_parameter_values():
         "Lithium interstitial reference concentration [mol.m-3]": 15.0,
         "Initial inner SEI thickness [m]": 0.0,
         "Initial outer SEI thickness [m]": 5e-09,
+        "Initial inner SEI on cracks thickness [m]": 0,
+        "Initial outer SEI on cracks thickness [m]": 5e-13,  # avoid division by zero
         "EC initial concentration in electrolyte [mol.m-3]": 4541.0,
         "EC diffusivity [m2.s-1]": 2e-18,
         "SEI kinetic rate constant [m.s-1]": 1e-12,
diff --git a/pybamm/input/parameters/lithium_ion/OKane2022_graphite_SiOx_halfcell.py b/pybamm/input/parameters/lithium_ion/OKane2022_graphite_SiOx_halfcell.py
index fe9d444874..35533ba80e 100644
--- a/pybamm/input/parameters/lithium_ion/OKane2022_graphite_SiOx_halfcell.py
+++ b/pybamm/input/parameters/lithium_ion/OKane2022_graphite_SiOx_halfcell.py
@@ -422,6 +422,8 @@ def get_parameter_values():
         "Lithium interstitial reference concentration [mol.m-3]": 15.0,
         "Initial inner SEI thickness [m]": 0.0,
         "Initial outer SEI thickness [m]": 5e-09,
+        "Initial inner SEI on cracks thickness [m]": 0,
+        "Initial outer SEI on cracks thickness [m]": 5e-13,  # avoid division by zero
         "EC initial concentration in electrolyte [mol.m-3]": 4541.0,
         "EC diffusivity [m2.s-1]": 2e-18,
         "SEI kinetic rate constant [m.s-1]": 1e-12,
diff --git a/pybamm/parameters/lithium_ion_parameters.py b/pybamm/parameters/lithium_ion_parameters.py
index 4ee8953c99..8d69ec49ca 100644
--- a/pybamm/parameters/lithium_ion_parameters.py
+++ b/pybamm/parameters/lithium_ion_parameters.py
@@ -416,11 +416,12 @@ def _set_parameters(self):
         )
         self.L_inner_0 = pybamm.Parameter(f"{pref}Initial inner SEI thickness [m]")
         self.L_outer_0 = pybamm.Parameter(f"{pref}Initial outer SEI thickness [m]")
-
-        # Dividing by 10000 makes initial condition effectively zero
-        # without triggering division by zero errors
-        self.L_inner_crack_0 = self.L_inner_0 / 10000
-        self.L_outer_crack_0 = self.L_outer_0 / 10000
+        self.L_inner_crack_0 = pybamm.Parameter(
+            f"{pref}Initial inner SEI on cracks thickness [m]"
+        )
+        self.L_outer_crack_0 = pybamm.Parameter(
+            f"{pref}Initial outer SEI on cracks thickness [m]"
+        )
 
         self.L_sei_0 = self.L_inner_0 + self.L_outer_0
         self.E_sei = pybamm.Parameter(f"{pref}SEI growth activation energy [J.mol-1]")