The displacement fields of different kinds of both perfect and dissociated dislocations have been calculated for an isotropic continuum, and by means of linear elasticity. Additionally, the corresponding HRTEM images have been simulated by the well-established EMS program package in order to predetermine the structural aspects of dislocations, and then to compare it with experimental HRTEM micrographs. The latter ones resulted from plastically deformed GaP single crystals and InAs/(OOl)GaAs single epitaxial layers. It could be established that using the simple approach of linear elasticity and isotropy results can be obtained which correspond well to the experimental images. So, the structure of various Shockley partial dislocations bounding a stacking fault can be detected unambiguously. The splitting behaviour of perfect 30" dislocations (separation into a 0" and 60" partial) and 90" dislocations (separation into two 60" partials) both with line direction along (112), 60" dislocations (separation into 3Oo/9O6 and 90"/30" configuration) and screw dislocations (separation into two 30" partials) along (110) are discussed in the more detail. Moreover, the undissociated sessile Lomer dislocation, glissile 60" dislocation and edge dislocation have been considered too.