Summary: The inverse problem of identification of boundary layer thickness is replaced by the higher-order boundary value problem for the Euler-Lagrange equation for minimization of the quadratic functional of the original system (method of variational imbedding). The imbedding problem is correct in the sense of Hadamard and consists of an explicit differential equation for the boundary layer thickness. The existence and uniqueness of solution of the linearized imbedding problem are demonstrated, and a difference scheme of splitting type is proposed for its numerical solution. The performance of the technique is demonstrated for three different boundary layer problems: the Blasius problem, flow in the vicinity of plane stagnation point, and the flow in the leading stagnation point on a circular cylinder. Comparisons with self-similar solutions where available are quantitatively very good.