Abstract: The numerical method of mechanical problems for the viscoelastic solids withRiemann-Liouville fractional derivative model is presented in this paper.Instead of using finite Grunwald definition of fractional derivative toapproximate the Riemann-Liouville's, this work has developed a numericalalgorithm directly from Riemann-Liouville's definition by taking advantagesof the features of its integrand kernel, assuming the approximating functionfor the integrand and making use of Newmark-type numerical methods. Thenumerical formulations are used to analyze the transient dynamic responsefor a viscoelastic oscillator and the finite element analysis procedures.The sample results show that the proposed method possesses the advantages offast convergence, higher accuracy, higher stability and easy for applicationand further modification.