In this paper, a method of analysis for steady viscous flow past a body in an infinite domain is proposed on a matching method of inner and outer solutions which may be regarded as an extension of the method of superposition proposed by the present authors. Viscous flow under consideration are described by the Navier-Stokes equations and the equation of continuity together with appropriate boundary conditions on the body surface and at infinity. It is, however, difficult to solve this nonlinear boundary value problem in an infinite domain, although the finite-element and finite-difference methods are effective tools for solving the Navier-Stokes equations in a restricted domain. If the far field solutions of the governing equations are given properly, the domain of numerical analysis for the Navier -Stokes equations is reduced to the finite one by the use of the method of matching inner and outer solutions. Assuming that the disturbance caused by an obstacle is small, Oseen linearized the Navier-Stokes equations, and the resulting equations can be solved in an analytical form. Oseen's approximation becomes highly accurate at a far distance from the body. Moreover, in the case of two-dimensions, Imai proposed an asymptotic solution on the basis of the Navier-Stokes equations by the successive approximation. In the present method, the infinite domain of analysis is divided into the inner and outer domain by introducing a fictitious surface. Oseen and Imai's approximate solutions can be used for the outer domain. The inner solution is given by solving the Navier-Stokes equations by the finite-element method and is matched on a fictitious surface with the outer solution. The present method is applied to two-dimensional and axi-symmetric problems including the practical analysis of the force acting on the mushroom anchor in the mud which can be regarded as viscous fluid. The validity of the present method is illustrated by numerical studios on the flows past a circular cylinder and a sphere whose results are in fairly good agreement with experiments by the previous authors.