A new method for numerical simulation of flame propagation in turbulent premixed combustible gaseous mixtures is proposed and tested. The method combines (I) a modified eikonal equation, employed to model the flame front dynamics; (2) a method of front tracking using a strip of computational cells containing the flame; and (3) a formula for turbulent flame propagation speed. The method includes two separate models. The first one obviates the necessity to solve equations for heat release, temperature and enthalpy, and utilizes a model equation of state to accurately render the volumetric effect and related instabilities. The second one provides a model for direct heal release and temperature calculation in the presence of heat-conducting boundaries (walls), in the multi-component combustible mixtures with variable composition and temperature-dependent heat capacities of all species. This model can be used when the heat transport on the walls is of interest, effects of flame quenching are essential and for the especially important case of combustion in a closed volume, e.g., in a cylinder of an internal combustion engine or chemical reactor. This modification is also effective for simulation of ramjet engines. The new method proves to be self-consistent, robust and highly effective.