Abstract We present a fitting technique that fits trace data into a generalized Erlang distribution class using an EM method. A generalized Erlang (GEr) distribution can be made by convolution of the third order ME distributions similar to the formulation of an Erlang distribution with exponential distributions. We give a sufficient condition for the representation to make a probability density function and we implement a fitting algorithm into a GEr distribution set by solving a nonlinear optimization problem with the EM algorithm. The effectiveness of the proposed fitting algorithm is presented by applying fitting methods to sets of synthetic data and measurement data. We present comparative numerical simulation results of our approach and other methods.