In this paper we use different types of word problems to study characteristics of problem-solving processes, understood as a modeling process. We work with a model of comprehension and we propose a classification for word problems around the idea of scientific model. An experimental set of two types of problems is constructed in relation to the explicit presence of the scientific model in the statement: undefined and well-defined. Subjects, two academics, were audio and video-taped during a problem-solving interview. The analysis of the interviews supports the hypothesis that differences in the statements generate different problem-solving processes. These differences seem to be associated with conceptual modeling skills. These results highlight some significant issues to be considered by teachers when selecting problems. We discuss criteria to guide the selection of one or another type of statement.