In base-isolated structures specially designed isolation systems provide the needed flexibility and energy dissipation capacity. The isolation systems, which can be either elastomeric or sliding systems, exhibit highly nonlinear behavior. The existing algorithms cannot analyze base-isolated structures with sliding isolation systems accurately. This paper presents an analytical model and a solution algorithm developed for nonlinear dynamic analysis of three-dimensional-base-isolated structures with elastomeric and/or sliding isolation systems. The novelty of the analytical model and solution algorithm is its capability to capture the highly nonlinear frictional behavior of sliding isolation systems in plane motion. Nonlinear behavior is restricted to the base and the superstructure is considered to be elastic at all times. Biaxial and uniaxial models, which can represent both elastomeric and sliding isolation bearings, are presented. The solution algorithm consisting of the pseudoforce method with iteration is presented. Comparison of computed results with experimental results is presented for verification. A six-story-reinforced-concrete-base-isolated structure is analyzed.