This study presents a theoretical analysis of the single-pressure straightening process for large-scale pipes, addressing the challenges of inadequate straightening precision and low efficiency associated with the current practice, which heavily relies on operator expertise. The straightening process of pipes through pressure is fundamentally a symmetrical three-point bending elastic–plastic deformation process. With the assumption of small deformations, the symmetric three-point bending of the pipe can be divided into two distinct deformation stages: fully elastic and elastic–plastic. For each stage, calculation models are developed, yielding the deflection formulae for any point on the pipe before and after unloading under varying punch strokes. The accuracy and reliability of the theoretical models are confirmed through finite element analysis and physical simulation experiments on smaller pipes. These models enhance the accuracy of single-pressure straightening and lay the groundwork for online material performance parameter identification based on load–stroke curves during the initial straightening phase. Both theoretical analysis and experimental outcomes demonstrate that the relationship between the maximum deflection after springback and the punch stroke are nearly linear, offering a practical method for developing intelligent control systems for pressure straightening.