Abstract: Based on Monte-Carlo simulations, the probability characteristics of cross-section capability of RC pier such as yield curvature, ultimate curvature, yield moment, ultimate moment, curvature ductility, plastic rotation angle and anti-shear capability, are studied. Results show that normal distribution can be used to model yield curvature, yield moment, ultimate moment and anti-shear capability; Gumbel distribution can be used to model ultimate curvature; and lognormal distribution can be used to model curvature ductility and plastic rotation angle. The influences of axial force variations on the probability distributions and the variability of the capability are also analyzed. It is seen that the probability distributions are independent of axial force variations, but dependent upon the variability. For yield curvature, yield moment and ultimate moment, the variation coefficients decrease with the increase of axial force. For ultimate curvature, curvature ductility and plastic rotation angle, the variation coefficients increase with the increase of axial force.