An analytical theory for the structure of corotating interaction regions (CIRs) in the solar wind is developed. First, an approximate stream interface is determined by mapping the curve dividing fast and slow streams at the solar wind source surface into the solar wind, at the slow solar wind speed assuming a constant angular rotation rate of the Sun. The flow of the fast wind then impinges on this surface, creating a quasi-perpendicular reverse (forward) shock in the fast (slow) stream, deflections of the shocked fast and slow flows tangential to the interface, and a modified location of the interface. Assuming a locally planar geometry and weak shocks, analytical expressions are derived and presented for both shock compression ratios and for the north-south and east-west components of the shocked fast and slow streams. These are evaluated for two representative curves dividing fast and slow streams at the solar wind source surface. Numerical results are also presented for shocks which may not be approximated as weak. It is shown that the weak shock approximation is valid well beyond its formal limit of validity. For characteristic solar wind parameters the shock and flow parameters are presented as functions of heliocentric radial distance r and the inclination of the stream interface at the solar wind source surface. Shock and flow parameters are also shown for a simulated spacecraft observation of a CIR at r=5 AU during a 26-day solar rotation period. The results of the model for the shocks and flows associated with CIRs are in apparent general agreement with observations by Ulysses and other spacecraft. ¿ 2000 American Geophysical Union