Dyke injection is a fundamental process of magma transport in the crust, occurring in all tectonic settings. The effect of extensional stress regimes on dyke injections is particularly important to understanding a wide spectrum of processes including continental rifting and volcanic activity. Yet dyke injection in extensional regimes has been relatively understudied. In addition, the effect of dyke-dyke interaction modifying the surrounding stress field and leading to dyke rotation about the vertical axis has not been addressed. We present the results from 23 laboratory analogue experiments investigating lateral dyke injections in a remote extensional stress field. This study is unique in that it addresses the effect of both extension and dyke-dyke interaction on the lateral propagation and rotation of dykes. The experiments study the interrelationship between successive lateral dyke injections by examining dyke injection thickness, injection spacing, injection orientation, extension, and structural relationship. A relationship between the rotation angle between two successive intrusions and the distance separating them under given extensional stress conditions is established. The rotation angle depends on two dimensionless numbers: the ratio of fluid overpressure of the first injection and remote tensile stress, and the ratio of the spacing between injections and the height of the first intrusion. The experiments show how the stress field is perturbed by an intrusion and how the remote stress field is locally relieved by this intrusion. The results show furthermore that measuring or estimating the rotation angles between successive intrusions within rift zones allows the spatial distribution of these intrusions to be estimated. In the case of the actively spreading Red Sea rift in Afar, Ethiopia, we find that the vast majority of the dykes are predicted to intrude within 10 km of each other and most frequently between 4 and 5 km, in good agreement with independent geophysical observations.