Bradley and Dudeney's model of the vertical distribution of the ionospheric electron concentration consists of three distinct sections. Both theE-region andF2-region are described by parabolic variations. A linear increase is assumed to exist between theE-region peak and theF2-region. This model is currently recommended by the International Radio Consultative Committee (CCIR) for use in long-term HF sky-wave prediction work. If a slightly modified electron-concentration profile is adopted, it is possible to derive exact expressions which describe some important characteristics of oblique ray paths in the model ionosphere. Ground range, group path, phase path and apogee height can all be computed using this technique. Collisions and the effect of the earth's magnetic field are ignored. These expressions have been used for several applications where a knowledge of multipath structure on ionospheric paths is necessary.