We have general knowledge of the principles by which catalysts accelerate the rate of chemical reactions but no precise understanding of the geometrical and physical constraints to which their design is subject. To analyze these constraints, we introduce a minimal model of catalysis based on elastic networks where the implications of the geometry and flexibility of a catalyst can be studied systematically. The model demonstrates the relevance and limitations of the principle of transition-state stabilization: optimal catalysts are found to have a geometry complementary to the transition state but a degree of flexibility that nontrivially depends on the parameters of the reaction as well as on external parameters such as the concentrations of reactants and products. The results illustrate how simple physical models can provide valuable insights into the design of catalysts.