Rock joints have significant effects on wave propagation. When the joints are filled with saturated sand or clay, the filling materials exhibit viscoelastic behavior on wave propagation. In the present study, wave propagation across single and multiple parallel joints filled with viscoelastic medium is examined. Based on a layered medium model, the recursive method is adopted and a modification is made under some special conditions for faster calculation. In the theoretical formulation, analytical solutions of wave propagation across a single viscoelastic joint as well as elastic joint are mathematically derived. Through parametric studies, it is found that the more viscous the filled medium is, the less the wave energy transmits. Meanwhile, distinct stop-pass behavior exhibits with the change of joint thickness or wave frequency for a single elastic joint. While for the wave transmission across a single viscoelastic joint, the transmission coefficient generally decreases with increasing joint thickness or wave frequency, except when the two parameters match with the pass bands of the corresponding elastic joint. When parallel joints exist, multiple wave reflections among joints influence wave transmission. The transmission coefficient decreases with increasing joint number and, the stop-pass behavior for viscoelastic joints is less significant than that for the elastic joints.