In this paper, we present an exploratory study on the evaluation of reliability levels associated with the piping design equations specified by ASME Boiler and Pressure Vessel (BPV) Code, Section III. Probabilistic analyses are conducted to evaluate reliability levels in straight pipe segments with respect to performance functions that characterize the different failure criteria using advanced first-order reliability method (AFORM). One important failure criterion considered in this study relates to the plastic instability which forms the basis of piping design equations for emergency and faulted load level conditions as defined in the ASME code. The code-specified definition of plastic instability is based on the evaluation of a collapse moment which is defined using the moment–curvature curve for a particular component. In this study, we use elastic-perfectly plastic, bilinear kinematic hardening, and multilinear kinematic hardening stress–strain curves to develop closed-form expressions for the moment–curvature relationship in a straight unpressurized pipe. Both the pressurized and the unpressurized loading conditions are considered. The closed-form reliability is evaluated using Monte Carlo simulation because of the complex nature of the closed-form expression. The reliability values are calculated with respect to the maximum allowable moment specified by the code design equations that use deterministic safety factors.