Abstract: A novel method based on B-differentiable equations is proposed to solve the elastoplastic dynamic contact problems with friction. The contact conditions are expressed in the form of B-differentiable equations, which can exactly satisfy Coulomb’s law of friction. By nesting the contact solution in the iterative process of constitutive equations, the number of solutions for contact flexibility matrix, which changes with stiffness matrix, is reduced significantly, further resulting in a shorter computational time. In addition, the damped Newton-Raphson method with 1D Armijo type linear search is applied in the solution of contact equations, which provides a good numerical convergence. Through a comparison with the commercial software ANSYS, the accuracy of the proposed algorithm is verified in two numerical examples, and the practicality and robustness of the method are supported in an engineering example.