Servo-actuated presses may provide maximum pressing force at any ram position in the same manner that hydraulic presses do, while offering several benefits in terms of precision, energy-conversion efficiency, and simplicity, due to their lack of hydraulic circuitry and oil. Several press builders have developed servo-actuated presses; however, issues relating to overconstrained multi-axis architecture have been disregarded. This study proposes an innovative method to avoid overconstrained architectures in multi-axis presses, by implementing a family of modular parallel mechanisms that connect multiple servo-axes to the press ram. Parallel mechanisms, which can be applied in several fields of robotics and industrial automation, exhibit important benefits for the application at hand, including high-load capacity, stiffness, and compactness. A biaxial industrial servo press prototype with a nonoverconstrained and modular architecture was built and presented as a proof of concept. Each axis comprises a servomotor, a gearbox reducer, and a ball-screw transmission. It is shown that such a press may be constructed from commercially available components, achieving high energy efficiency and high press force with relatively simple construction. A direct comparison with an equivalent hydraulic-press model is carried out, thus highlighting the servo press energy efficiency.