Tuned Mass Damper (TMD) are commonly used to control seismic and wind vibration of structures. Traditionally, linear TMDs are considered and they have certain optimum parameters. If TMD is considered to be elasto-plastic, then, it is expected that energy absorbing capacity of TMD will increase. In this work, linear TMD with optimum parameters based on equal eigenvalue (EEV) criterion is used and is considered to be elasto-plastic. In EEV, TMD parameters are obtained by equating eigenvalues of two modes. Damping and stiffness corresponding to EEV criterion is taken and for the elasto-plastic TMD, the yield level is changed. The nonlinear equations of motion are solved numerically, using the Newmark-Beeta method using a code written in MATLAB. Results on comparison of performance of elasto-plastic TMD and an elastic TMD are obtained. Effect of yield level of elasto-plastic TMD on the response of main system and TMD is studied.