We present a novel new method for modelling magnetized molecular cloud cores using submillimetre linear polarization maps from thermal dust emission. Our PolCat modelling software builds a three-dimensional core model via the use of consecutive parametrized coordinate transformations, and produces simulated polarization maps to fit to observational datasets. We utilize the Ferret evolutionary optimizer to search the parameter space to simultaneously minimize chi-squared for the intensity and polarization position angle maps separately. We have applied PolCat to multiple test problems and several datasets from the SCUPOL Legacy Catalogue. We find that PolCat is able to distinguish between maps of twisted and non-twisted field geometries and identify twist symmetry. Preliminary fits to several datasets show that the best potential field geometries to our sample cores contain field twists. Further research using a larger number of maps is required to determine if twisted fields are commonplace in cores.