As the desire for high performance buildings increases, a number of solutions to enhance the dynamic response of structures have been explored and implemented. In recent years, base isolation has become a practical and effective strategy for earthquake resistant design. To this end, a number of isolation solutions are currently available. Among these, laminated lead rubber bearings and friction pendulum devices have been most widely used in the last 25 years. Recent studies have explored the possibility of employing flat or curved sliding-surface base isolators with variable friction coefficients. These new types of devices have been shown to be capable of performing theoretically better than traditional sliding isolators in light of their higher energy-absorption capacity. This paper provides insight into the mechanics of variable friction sliding isolators, exploring viable ways of dealing with these types of elements from a numerical point of view. A number of 2D non-linear time history analyses, in which the new elements are treated as non-linear translational spring elements, are conducted and the results are discussed in detail.