This investigation focuses on the development and exemplification of a comprehensive methodology for the inclusion of uncertainty in mass, stiffness, and post-yield properties in nonlinear dynamic analysis of structures exhibiting yielding. The maximum entropy-based nonparametric approach is proposed here for the statistical modeling of these uncertainties while the post-yield analysis is carried out using a recently introduced material degradation model. The structure chosen to exemplify the methodology is a 4-story shear frame analyzed in physical coordinates, the mass and stiffness matrices of which exhibit specific topological constraints. The inclusion of these particular constraints within the maximum entropy framework is first performed and a comparison is next made between the responses of uncertain linear shear frames satisfying and violating the topology constraints. Surprisingly, it is found that the power spectra of the responses are extremely close suggesting for this structure that a slight violation of the topology by the uncertainty model has only a small effect. The topology-preserving uncertainty model is then used with the degradation model to assess the effects on the response of the yielding structure of uncertainty in mass, linear stiffness matrix, and stiffness matrix and post-yield behavior. In all cases, a small level of uncertainty was found to have a very significant effect on all aspects of the structural response. The uncertainties in stiffness properties were found to affect much more the post-yield response (e.g. maximum displacement after yield) than those in mass but have approximately equal effects on the power spectra of the displacements.