Summary: We use a general method for calculation of asymptotics of solutions of nonlinear algebraic and ordinary differential equations which is based on the geometry of power exponents, including the Newton polyhedron. The method gives strictly mathematical backgrounds for the boundary layer theory. We study the plane stationary viscous fluid flow around a semi-infinite flat plate with the boundary condition in infinity, which is the flow parallel to the plate. Considering the solution and boundary conditions from the viewpoint of the geometry of power exponents, we obtain the first and second asymptotic approximations of the stream function in the boundary layer, at the infinity and near the edge of the plate. They coincide with classical results.