A piecewise polynomial collocation approximation of the shape function is applied to Volterra’s form of the quasi-static equations. This formulation of the quasi-static method does not require the imposition of an arbitrary constraint. The resulting set of nonlinear unconstrained quasi-static (UQS) equations is solved by using fixed-point iteration. The shape equation, which is similar in form to those obtained by using Padé’s algorithms, is solved with a second-order variational minimization technique. The results of this formulation are then compared with other quasi-static solutions for a typical Canada deuterium uranium (CANDU) reactor safety analysis calculation.