The spinning rotor gauge has found increasing use in ultrahigh vacuum measurements, but it also could be attractive in higher pressure regimes provided an accurate theory were available for interpretation of the measurements (that is, the torque or the deceleration rate as a function of the pressure). In this article we numerically solve the Stokes equation with slip boundary conditions for the rotor geometry by using a Green’s function based approach. We verify that the numerical technique provides accurate results, and then we discuss how the rotor gauge can be used for measurements of the viscosity, the velocity slip coefficient, and the tangential momentum accommodation coefficient. A companion article describes experimental measurements and results for several gases.