An extension of the coupled criterion (CC) of finite fracture mechanics is established in order to assess dynamic crack initiation. The main change compared to the classical quasi-static approach consists in considering the crack velocity profile during initiation instead of assuming an instantaneous crack initiation. The proposed approach enables the study of dynamic crack initiation under either quasi-static or dynamic loading. It is illustrated on several examples including transverse cracking in laminates, crack initiation in drilled specimen under quasi-static tension or compression and on a V-notch specimen subjected to time-dependent loading. The dynamic CC predicts crack initiation over a finite length occurring in a given time depending on the crack velocity. The influence of the initiation crack velocity profile is significative provided crack velocity is large enough. Taking into account dynamic effects enables a better representation of experimentally observed variation of initiation stress as a function of hole size under tensile loading in drilled hole specimens.