Extensive shock and highly localised blast waves generated by detonation of near field explosives (such as Improvised Explosive Devices (IED's)) are catastrophic to structures and detrimental to humans and may result in injury or death, penetration and progressive damage, or perforation through the structure and collapse. Mitigating the effects of such waves is paramount in various aspects of design in Structural, Aeronautical, and Defense engineering, as well as being useful in Forensic Sciences. A theoretical model is presented here to predict the large inelastic deformation of ductile thin square membranes induced by a generic short duration localised pressure pulse load. The pulse loading was idealised as a multiplicative decomposition of spatial and temporal functions. The spatial part is a piecewise continuous function of axisymmetric distribution of constant pressure over a central zone of the target, then exponentially decaying beyond this zone. The temporal part may assume various shapes. Using the constitutive framework of limit analysis and incorporating the influence of finite displacements, two patterns of kinematically admissible, time dependent velocity profiles were investigated. These patterns included stationery and moving plastic hinges. The results were investigated in two cases: once with the interaction between bending moment and membrane forces retained in the analyses, and then when the response was solely governed by membrane forces. For blast loads of high magnitude, the pressure was replaced by an impulsive velocity and the results were cast as functions of dimensionless form of initial kinetic energy. The theoretical results corroborated well with the available experimental results on high strength ARMOX steel, a class of steel impervious to the phenomenon of rate sensitivity.