It is investigated if the mental computation strategies in the research literature are enough to satisfactorily categorize the mental computation strategy use by preservice elementary teachers in multiplication on one- and two-digit natural numbers. The preservice elementary teachers use of mental computation strategies is measured operationally with a written questionnaire. The paper indicates that there are few new strategies used by preservice elementary teachers which are not already contained in the research literature. However, the paper indicates that there is a theoretical need to clarify the strategy definitions, and that there several useful and valuable strategies on multiplication that do not occur in the research literature on mental computation.