This is the nonideal (Delta') version of the Princeton Equilibrium and STability (PEST) suite of codes, which has been developed since the late 1970s to determine the linear stability properties of toroidal, magnetically confined plasma equilibria. PEST3 assumes zero-inertia for all components of the displacement. The result is a displacement field that is strongly singular (i.e. non-square integrable) about rational surfaces. The leading coefficients of the dominant and recessive components of the normal displacement are extracted to form a matching (Delta'-)matrix, which can be used in a postprocessing stage to determine the nonideal stability of linear or weakly nonlinear modes. Modes that fall in this category are the nonlinear resistive and neoclassical tearing modes for instance, provided the island width is small compared to the minor radius. In addition to computing the matching data, PEST3 also returns a yes/no answer to the ideal stability question.