A 2D version of a 3D nonhydrostasic finite-difference meteorological model is compared with a 2D finite-element model used to simulate the effects of atmospheric front propagation over a 2D valley. The front surface is described in the models by an equation for advection of a scalar substance, which is solved by a third-order semi-Lagrangian procedure. A leap-frog type scheme in combination with an Asselin filter is used for time discretization. Special operators of space discretization are used to provide conservation of momentum and scalars in the finite-difference model. Triangular elements are used in the finite-element model. The results of 2D model simulations show reasonable behavior of cold front propagation over a valley as calculated by both models. The FEM model seems more universal in describing complicated surf aces, although with the FDM model it is easier to conserve the invariants of the initial differential equation system.