This paper presents the development and verification of a collision probability (CP) code, capable of modelling neutron transport in one-dimensional slabs and axially heterogeneous cylinders with varying radii. The CP code is used to model layered systems of aqueous and organic plutonium nitrate, as process criticality accidents are more likely to occur in these systems compared to dry systems. The use of the CP code is desired as it offers a computationally inexpensive method for calculating neutron transport when compared to higher fidelity codes such as MCNP. For slab geometries, the CP code can be used effectively, given they contain at least 0.7 g cm−2 plutonium. The approximation employed by the CP code to model heterogeneous cylinders overestimated the rate of radial neutron leakage such that vessels with radii of 30.0 cm could not reliably calculate reactivity to within 1 $ of MCNP. Increasing the radii to 40.0 cm improved the accuracy of the CP code to within 1 $ of MCNP for systems containing at least 2.75 kg plutonium. The error in the CP code increased when used to model cylindrical geometries with dished ends and complete vessels with dished ends, such that systems with large dished ends and low plutonium content should be avoided. As a simple, neutronics based model, the CP code could be used as part of rough order of magnitude calculations for criticality transients, where high levels of accuracy are not required, given that potential errors in results have been previously identified.