Important and critical structures should be designed to resist transient extreme loads such as high velocity impacts and explosions. Blast-resistant design of structures includes architectural design and structural design against explosion forces. Blast loads could be internal due to explosion of gas pipes or external due to chemical bombs and car attacks. During the last few years, Egypt witnessed terrorist bombs and car attacks on important structures. These events caused large life losses and led to severe damage and collapse of several heritage and security buildings. In this paper, the response and damage of single-degree-of-freedom (SDOF) structures to blast loads are presented. The blast load is modeled as a time-variant function with positive and negative pressure zones. Firstly, the governing nonlinear differential equation of motion for SDOF of inelastic structures under blast load is provided. Subsequently, the solution of this equation is obtained using numerical integration of the equation of motion in the MATLAB platform [1]. Finally, the definition of various energy terms dissipated by the structure and associated damage indices are given. The formulation developed is numerically demonstrated with reference to energy dissipated and damage of a simple structure modeled as a SDOF inelastic system to blast load. A new scalar index based on damage indices is proposed. These measures are of essential importance since they provide quantitative measures on damage level of the structure and necessary repair.