This dissertation aims to provide a better understanding of seismic sidesway collapse of highly inelastic basic structure vulnerable to the destabilizing effect of gravity loads (i.e., the P-delta effect), and to enhance the prediction of their seismic collapse capacity with simple measures.A major part of this dissertation is devoted to the quantification of the collapse capacity uncertainty of P-delta vulnerable single-degree-of-freedom (SDOF) systems. In particular, the reduction of record-to-record variability (RTR) of the collapse capacity is addressed through an appropriate choice of the intensity measure (IM) of the earthquake excitation. The effect of uncertainty of the main characteristic parameter responsible for seismic induced global collapse, i.e. a post-yield negative stiffness ratio, on the median and the dispersion of the collapse capacity is quantified. The impact of the characteristic structural parameters and various IMs on the collapse capacity and its RTR variability of P-delta sensitive multi-degree-of-freedom systems is studied. Design collapse capacity spectra and fragility curves with reduced RTR dispersion based on the proposed “average” IM, refined collapse capacity spectra and fragility curves based on a conventional IM, and analytical parameter dispersion collapse capacity spectra are provided through multiple regression analysis, aiming to enhance the simplified assessment of P-delta vulnerable systems within the general framework of the collapse capacity spectrum methodology.