The flow of a stratified fluid past three-dimensional (3D) obstacles at intermediate Rossby number (Ro approximately unity) is studied using linear semi-analytic calculations and nonlinear numerical simulations. Linear solutions are obtained using a Fourier transform approach combined with a recently developed methodology for computing accurate numerical approximations to the singular Fourier inversion integrals. Using this technique, the change in the linear flow patterns is explored as the Rossby number is gradually decreased from roughly Ro=10 (essentially nonrotating flow) to Ro=0.1 (essentially quasi-geostrophic flow). This regime of intermediate-Rossby-number disturbances has previously received little attention in the case of 3D flows. The linear solutions are then compared to nonlinear numerical simulations at finite obstacle height in an effort to identify important nonlinear effects.