The effect of vapor cavitation on the pressure distribution and the force coefficients of a long squeeze film damper executing circular centered orbits is studied in association with the Swift-Stieber cavitation boundary conditions. The existence of vapor cavitation significantly decreases the whole of the pressure distribution. A modified Reynolds equation is solved analytically for a long squeeze film damper to investigate the effect of fluid inertia on cavitated pressure profiles. Increasing fluid inertia lends to extend the region of cavitation to the minimum film gap and to reduce the pressure. The corresponding damping and inertia force coefficients are presented for varying positions of cavitation inception and termination. Experimental comparisons are presented in Part II.