Search is a basic activity that is performed routinely in many different tasks. In the context of medical imaging it involves locating lesions in images under conditions of uncertainty regarding the number and locations of lesions that may be present. A search model is presented that applies to situations, as in the free-response paradigm, where on each image the number of normal regions that could be mistaken for lesions is unknown, and the number of observer generated localizations of suspicious regions (marks) is unpredictable. The search model is based on a two-stage model that has been proposed in the literature, according to which, at the first stage (the preattentive stage) the observer uses mainly peripheral vision to identify likely lesion candidates, and at the second stage the observer decides (i.e., cognitively evaluates) whether or not to report the candidates. The search model regards the unpredictable numbers of lesion and non-lesion localizations as random variables and models them via appropriate statistical distributions. The model has three parameters quantifying the lesion signal-to-noise ratio, the observer's expertise at rejecting non-lesion locations, and the observer's expertise at finding lesions. A figure-of-merit quantifying the observer's search performance is described. The search model bears a close resemblance to the initial detection and candidate analysis (IDCA) model that has been recently proposed for analysing computer aided detection (CAD) algorithms. The ability to analytically model and quantify the search process would enable more powerful assessment and optimization of performance in these activities, which could be highly significant.