The use of ultra‐high‐performance fiber reinforced concrete (UHPFRC) to repair or rehabilitate old concrete structures has been shown to be appropriate due to its properties, such as higher compressive strength, ductility, and durability than conventional concretes. One of the studied strengthening techniques is the reinforced concrete columns jacketing by UHPFRC. Some recent research evaluated some parameters, such as the repair thickness and the volumetric ratio of stirrups. However, other important parameters, such as UHPFRC jacketing thickness in different column cross‐sections and the concrete core compressive strength, need to be addressed. In addition, the analytical models presented in the literature are restricted to only one concrete grade. The present study aims to evaluate the behavior of short reinforced concrete columns strengthened with UHPFRC subjected to centered compression. Numerical analyses of three‐dimensional models were performed using the finite element method, validated, and calibrated using experimental results. The influence of the concrete core compressive strength, the UHPFRC jacketing thickness, and the shape of the cross‐section were evaluated. Numerical simulations concluded that the lower concrete core compressive strength columns showed the best relative increase performance. Moreover, the concrete core strength was inversely proportional to the resistance capacity of the repair system. In addition, the increase in repair thickness contributes to the axial strength of the column. Furthermore, the cross‐section influences the distribution of stresses and strains, showing the best performance for circular sections. Finally, regardless of cross‐section type, the proposed equations accurately predicted the numerical results.