beta-lactam antibiotics are the most commonly used antibiotics which cause bacterial cell lysis by inhibiting the enzyme responsible for the cell wall synthesis. Production of beta-lactamase enzyme, which catalyzes the hydrolysis of beta-lactam ring of beta-lactam antibiotics is the most common mechanism of bacterial resistance. beta-Lactamase Inhibitory Protein (BLIP), is an effective inhibitor of class A beta-lactamases such as TEM-1 and SHV-1. TEM-1 and SHV-1 are the most commonly found beta-lactamases and they are responsible for the resistance to beta-lactam antibiotics of various pathogenic bacteria. In an effort to elucidate the mechanism of beta-lactamase inhibiton by BLIP and to make predictions of binding affinity between these molecules, Molecular Dynamics (A D) simulations were performed on TEM-1 and SHV-1 bound to BLIP and BLIP based peptides. Asp49 residue which is known to play a critical role on binding on BLIP was mutated to Alanine to determine the contribution of this residue to binding. Binding free energy of the TEM-1 and SHV-1 bound BLIP, mutant BLIP (D49A) complexes were estimated by the molecular mechanics Poisson Boltzmann Surface Area method (MM-PBSA). Free energy of binding calculations show that the mutation on D49 causes a decrease in binding affinity for both TEM-1 and SHV-1 lactamase.