A novel one-dimensional (1D) model to account for the diffusion-reaction problem in catalytic pellets with arbitrary shape is proposed. The model includes three geometrical parameters, which are fitted by matching the behavior of the actual pellet at high and low Thiele moduli simultaneously. The formulation presented here for the diffusion-reaction problem with arbitrary pellet shapes and for the geometric ID approximation is intended for covering a wide range of cases, concerning kinetics (including thermal effects), transport models, and variable catalytic activity. In this contribution, the effect of critical geometrical ratios that is observed in some pellet shapes is focused on testing the performance of the ID model, assuming isothermal first-order kinetics. Remarkable precision (errors of <2%) was reached in all of the tested cases.