A numerical model capable of predicting the multi-dimensional laminar flames which occur on burners used in domestic appliances is described. The model is embodied in a computational fluid dynamics code, modified to include multi-step combustion chemistry. This is used to solve the appropriate fluid dynamic equations. The model involves a second-order accurate finite-volume method to allow accurate prediction of the detailed structure of flame fronts, with the computational cost of capturing such fine structures being reduced by employing an adaptive finite-volume grid algorithm coupled to a variety of reduced chemical kinetic schemes and transport property algorithms. Results derived from the complete model are used to demonstrate its ability to predict those parameters that are of importance in the design of laminar flame burners, and are shown to be similar to experimental results obtained on a realistic burner.