In this paper we detail the optical design of HIFI, one of three instruments to be flown on the Herschel Space Observatory and also outline the general approach taken in analysing the quasi-optical performance of the instrument. Gaussian Beam Mode Analysis theory is the principle technique chosen for the quasi-optical analysis, supplemented by the commercially available optical analysis package GLAD. These quasi-optical techniques are used for validation of the optical design and predicting the performance of the HIFI system. The HIFI system was checked for issues such as truncation, mechanical misalignment and aberrational losses, along with aperture efficiency and LO coupling efficiency. The quasi-optical analytical methods described could be applied generally to long wavelength optical instruments.