Currently, pumping systems-whether single-branch, multi-branch or networked, are among the most widespread applications in the field of fluid transport in areas such as the agro, marine and mining industries. For the proper economic exploitation of these systems, two aspects must be carefully evaluated: the structural design and the strategies adopted to ensure their reliability and efficiency. The key factors in the latter are the proper selection of the pump and the precise modeling of the fluid flow in the system. Nevertheless, little information is available on the mathematical models for even the simplest multi-branch systems: two parallel-branch with one single pump. The existing models typically simplify the system by not considering the suction branch. In the present study, a complete mathematical model was developed to include the suction branch in the analysis. Its solution is obtained in closed analytical form, and gives explicit equations to calculate the flow rates in each branch. The results obtained from the model were validated through comparison with numerical simulations carried out in AFT Fathom software. Different typical scenarios for the phenomenon under study were evaluated, allowing for variations in the elevation of the discharge reservoirs, the pipe length, roughness, and diameters. The results show a relative error between the numerical and analytical solutions for the total flow rate always below 1.5%. Regarding the flow rate distribution for each branch, the largest absolute error (around 2 L/s) was observed in the branch with the lowest flow rate. This discrepancy is due to the hypothesis of constant friction factors used in the development of the analytical model. From the results, it can be concluded that the proposed model accurately determines the total flow rate and the distribution for each system branch.