A standard approach to analysis of case-cohort data involves fitting log-linear models. In this paper, we describe how standard statistical software can be used to fit a broad class of general relative rate models to case-cohort data and derive confidence intervals. We focus on a case-cohort design in which a roster has been assembled and events ascertained but additional information needs to be collected on explanatory variables. The additional information is ascertained just for persons who experience the event of interest and for a sample of the cohort members enumerated at study entry. One appeal of such a case-cohort design is that this sample of the cohort may be used to support analyses of several outcomes. The ability to fit general relative rate models to case-cohort data may allow an investigator to reduce model misspecification in exposure-response analyses, fit models in which some factors have effects that are additive and others multiplicative, and facilitate estimation of relative excess risk due to interaction. We address model fitting for simple random sampling study designs as well as stratified designs. Data on lung cancer among radon-exposed men (Colorado Plateau uranium miners, 1950-1990) are used to illustrate these methods.