A new theory is presented for the radiation problem of heave and pitch modes of a slender ship advancing at arbitrary forward speed. The theory has no restrictions on the order of forward speed and oscillation frequency, embracing both of unified theory developed by Newman and high-speed slender-body theory (HSSBT). The inner velocity potential consists of a particular solution, which is the same as that of HSSBT, and a homogeneous component, which is constructed by the superposition of the real-flow velocity potential and the reverse-flow reverse-time velocity potential. Since precise computations of HSSBT are prerequisite for the present theory, the calculation procedure adopted for HSSBT is described, converting the formulation into an equivalent initial-value problem in the time domain and applying the higher-order boundary-element method at each time step. Numerical results of added-mass and damping coefficients based on the present theory are shown for a modified Wigley model and compared with corresponding experiments and other computed results by the strip method, HSSBT, and 3-D Rankine-panel method.