We consider the propagation speed of thin premixed flames disturbed by the fluid flow and suggest a new approach based on using the generalized curvilinear system of coordinates and tenser calculus. The suggested technique is shown to be more simple than the traditional technique used by Sivashinsky (1976), Matalon and Matkowsky (1982) and also in other publications. The result of Matalon and Matkowsky (1982) is generalized for an arbitrary temperature dependent diffusion coefficient.