A random vibration method is developed for the response analysis of multistory buildings under stochastic bi-directional earthquake motions. The biaxial hysteretic restoring force is modeled by coupled nonlinear differential equations; the response statistics are obtained using the equivalent linearization method. The complete solution for SDOF systems and the basic formulation for MDOF systems are presented. The validity of the proposed hysteretic model is appraised using available biaxial loading test results of reinforced concrete columns.