This work presents experimental and computational studies on progressive failure analysis of notched cross-ply carbon fiber reinforced polymer (CFRP) composite. The carbon/epoxy composite laminated with [90/0]_s layup is tested using double-notched specimens loaded in tension. The load-displacement curve, failure load and damage patterns of all tested specimens are discussed. In addition, a numerical analysis approach based on material property degradation method (MPDM) and cohesive elements (CE) is illustrated to capture complex failure mechanisms and damage progression as observed in the tested specimens. The MPDM is used to model the in-plane failure of 90° plies and 0° plies while the cohesive elements are used to account for the delamination at the [90/0] interfaces. Different progressive failure models employing fracture mechanics, continuum mechanics and micromechanics of failure are presented based on the MPDM-CE approach. The failure analyses by these progressive models are performed and their predictions are compared with the experimental results of notched [90/0]_s CFRP composite. Reasonably good agreement between experimental results and simulation results is obtained and it is shown that the MPDM-CE approach can effectively predict the progressive failure of double-notched [90/0]_s composite laminate.