AbstractA constitutive operator split method with implicit‐explicit time integration is presented for the transient analysis of rigid block models of jointed media. The linear portion of the joint constitutive law is integrated by an implicit method and the non‐linear, time dependent portion is integrated by an explicit method. The method features the stability of implicit procedures as well as the flexibility of explicit procedures for non‐linear problems. The solutions obtained with this method are compared to the solutions obtained by the explicit central difference method; in all cases there is good to excellent agreement. For some problems, particularly for those with low frequency excitation, it is shown that the implicit‐explicit method can result in a substantial savings over more conventional explicit