A major difficulty for problems involving frictional contact is that the solution of the equilibrium equations must satisfy nonlinear inequality constraint conditions on the frictional contact boundary: non-interpenetration condition along the normal direction of the contact boundary and Coulomb frictional law in the sliding direction along the tangent line or tangent surface, in which constraints along these two directions are coupled to each other. To describe such a representative behavior which exactly satisfies these nonlinear inequality constraints for a generalized frictional contact, an incremental variational inequality is first described in this study. Subsequently, an effective linear complementary formulation is established after numerical discretization. A reduced number of unknown variables are employed which are the gap function and the norm of the incremental sliding displacements for the tangential directions with the Complementary variables chosen as the normal contact forces and relaxation variables in the tangential directions. Lemke's algorithm was employed to solve the resulting linear complementary equations. The present approach possesses high accuracy and involves features for reduced storage and computational cost. Another advantage of proposed methodology is that extensions to general frictional contact problems involving nonlinear and/or dynamic computations are permissible. Although the theoretical formulations shown here are valid for 3-D frictional contact, to sharpen the focus of the present study attention is confined here to linear elastic problem and for two dimensional validations only for the purposes of illustration. Numerical test models are presented which accurately satisfy the problem physics and contact conditions and therein validate the present developments.