Transverse magnetic (TM) and transverse electric (TE) wave transmissions of an oblique parallel-plate waveguide array is studied. The scattered wave is represented in terms of continuous and discrete modes based on the Fourier transform and series, respectively. The tangential field continuities at the boundary are enforced to obtain simultaneous equations for the discrete modal coefficients. Residue calculus is utilized to transform the radiation field and reflection coefficient into numerically efficient forms. Numerical computations are performed to illustrate the behavior of wave radiation and reception by an oblique waveguide array.