Software Effort estimation involves the estimation of effort required to develop software. Cost overrun, schedule overrun occur in the software development due to the wrong estimate made during the initial stage of software development. Proper estimation is very essential for successful completion of software development. Lot of estimation techniques available to estimate the effort in which neural network based estimation technique play a prominent role. Back propagation Network is the most widely used architecture. ELMAN neural network a recurrent type network can be used on par with Back propagation Network. For a good predictor system the difference between estimated effort and actual effort should be as low as possible. Data from historic project of NASA is used for training and testing. The experimental Results confirm that Back propagation algorithm is efficient than Elman neural network.