This paper presents an epoch extraction method from the phase spectrum of speech signals. The phase spectrum of speech is modelled as the response of an allpass (AP) system. The coefficients of AP system are estimated by imposing sparsity constraint on the input signal. The AP residual is estimated using orthogonal matching pursuit and it is found that the residual signal exhibits prominent peaks at epoch locations and negligible values elsewhere. A dynamic programming algorithm is employed to select appropriate peaks from AP residual corresponding to epoch locations. Epoch extraction performance of the proposed algorithm is evaluated on a subset of CMU Arctic database. The AP modelling based epoch extraction method is compared with two state-of-the-Art epoch identification techniques, namely DYPSA and zero frequency resonator (ZFR). It is observed that the proposed algorithm delivers equivalent performance as that of ZFR for clean speech and significantly out-performs ZFR for telephone speech. Also the AP modelling based method provided slightly better epoch identification rate than DYPSA for clean as well as telephone speech. © 2014 IEEE.