The slope discontinuity in C° contact formulation is known as the cause of iteration convergence difficulty in sliding contact. In this paper, a smooth contact surface representation is introduced to remove the slope discontinuity in a C° contact formulation. The non-uniqueness in the solution of closest point projection near the junction of C° surfaces is eliminated by this new approach. The smooth surface representation is incorporated into meshfree formulation to yield a consistent tangent operator for frictional contact problems. The proposed method is successfully applied to a sheet metal deep drawing problem involving large sliding contact and a sheet metal stamping problem.