Hydraulic press machines (HPMs) are a complex nonlinear system that work across a large operation region. In such a region, input/output samples do not easily satisfy the requirements of data-driven modeling because of many practical constraints involved. This renders HPMs difficult to model accurately. In this paper, an operation-region-decomposition-based SVD/NN modeling method is proposed for this type of system. It can produce models that work across a large operation region without input spectra with special properties. Using this method, this operation region is first broken down into a group of local operation regions. Every local region is excited by its corresponding input signal. Because the complexity of the system at the local region is much lower than the original system throughout the operation region, the required input signal for modeling at a local region is easier to obtain than the one suitable for the whole region. An SVD/NN modeling method is then proposed to produce a low-order model from these experiments at all local operation regions. Finally, a practical HPM experiment was used to demonstrate the effectiveness of the proposed method.