We present mathematical methods for the interpretation of high frequency radar sea‐echo measured by narrow‐beam and CODAR systems. (CODAR is a small transportable radar with a scanning broad beam). These methods are based Barrick's equations for the ocean radar cross section in terms of the directional ocean waveheight spectrum and surface current, using a dimensionless mathematical formulation. In this paper, we describe the simulation of narrow‐ and broad‐beam radar sea‐echo from both deep and shallow water, discussing the effect of ocean surface currents, including vertical and horizontal current shear. This paper provides the mathematical tools for the modeling of common experimental situations in HF radar oceanography; such models are used in subsequent papers that describe the extraction of sea‐state information from HF radar se