Bilinear and slip-type restoring force characteristics, which consist of normal bilinear hysteresis and slip-type hysteresis with tri-linear skeleton curve, are used as restoring force characteristics of wooden houses. A double impulse input can represent pulse-like ground motions recorded near earthquake source faults, and the closed-form solutions are derived for maximum deformation angles of a single-degree-of-freedom (SDOF) bilinear + slip system subjected to the critical double impulse input. Furthermore, the closed-form solutions can provide the simple evaluation method of the critical responses of two-story wooden houses subjected to near-fault pulse-like ground motions with reduction method to SDOF system.