We present a Resolution of Identity and Cholesky Decomposition Based Implementation of EOMMP2 approximation. The RI and CD based EOM-MP2 shows significant speed-up and less storage requirement than the conventional canonical version and can be applied to very large systems. The newalgorithm used for this implementation eliminates the most storage requiring four-index quantities resulting in the decrease of storage requirement, reduction in I/O penalties and improved parallel performance, at the expense of more floating point operations. Therefore, the speed-up compared to conventional EOM-MP2 method is more prominent in case of EA, EE and SF case where the storage bottleneck is significant than the EOM-IP-MP2 method, where thestorage requirement is significantly less. However, the RI/CD based EOM-IP-MP2 can be coupled with frozen natural orbitals to gain further speed-up.