The purpose of this paper was to investigate how it becomes possible for solvers to make drawings to advance their problem solving processes, in order to understand the use of drawings in mathematical problem solving more deeply. For this purpose, three examples in which drawings made by the solver played a critical role in the solutions have been analysed in detail. In particular, the prehistories of the drawings were taken into account in analysing those examples. The analysis illustrates that the solver could make well-designed drawings because of the information about the problem situations which had been obtained in previous activities. This result indicates that when discussing the use of drawings in mathematical problem solving, one should pay attention to the influence of the solvers' understanding concerning their use of drawings, as well as the influence of their use of drawings on their understanding.