The production of organic acids by biotechnological processes has experienced a notable impulse with the advent of first and second generation biorefineries and the need of searching for renewable and sustainable feedstock, such as biomass. Fumaric acid is a promising biomonomer for polyamide production and a well-known acidulant and preservative in food and feed industries. Malic acid is a well-known food acidulant with a high market share. The biotechnological Fumaric and Malic acid production via fungi of the Rhizopus genus is being explored nowadays as a process for the valorization of food and food-related waste to obtain food ingredients and key platform chemicals of the so-called biochemical biorefinery. In this work, a preliminary study is performed to find reproducible conditions for the production of the acids by Rhizopus arrhizus NRRL 1526 by controlling fungi morphology and inoculum conditions. Afterwards, several production runs are performed to obtain biomass, glucose, and acid concentration data at different processing time values. Finally, an unstructured, unsegregated model including a logistic-type equation for biomass and potential-type equations for the substrate and the products is fitted to experimental data. We find that the production of the organic acids is mainly non-associated with fungal growth.