Power supply to trains, subways and trams is mainly provided by systems known as flexible catenary and rigid catenary. Flexible catenary has been extensively studied, while rigid catenary has received much less attention. This paper studies the contact forces between the pantograph and the rigid catenary in systems using more than one pantograph. Lumped-element models of pantograph and a finite-element model of catenary have been used for this purpose. Different speeds and a wide range of distances between pantographs have been simulated. The results show that, in general, front contact forces are lower than rear contact forces. Furthermore, the use of more than one pantograph can help to reduce contact forces as long as the spacing and span length are accounted for. It is also observed that the use of different pantographs does not provide significant advantages. A relevant result is that an appropriate selection of the pantograph model used and pantograph spacing can lead, in certain cases, to a reduction of contact forces at high speed, which would reduce wear, improve safety and extend the range of speeds in which the rigid catenary can operate.