New expressions for the stress field of straight dislocation segments are derived from the de Wit's expressions for an infinite straight dislocation. Restricted to linear isotropic elasticity, these compact formulae are given in tensor and vector notation expressed in an arbitrary Cartesian reference frame. This solution, allows to compute the internal stress fields or the dislocation-dislocation interactions involved in three-dimensional simulations of plastic strain at spatial scales involving large numbers of dislocations.