Fast liquid jets are investigated for use as a needle-free drug delivery system into an elastic tissue such as skin. Using smaller jet diameters in a repetitive regime can mitigate bruising and pain associated with current injectors. In this study, we aim to unravel the potential of the method to deliver liquids into biological tissues having higher elasticity than healthy skin (i.e >60 kPa). To address this challenge, we have implemented a laser-based jetting system capable of generating supersonic liquid microjets in a repetitive regime. We provide insights on the penetration of microjets into hydrogel samples with elastic modulus ranging from 16 kPa to 0.5 MPa. The unprecedented speeds of injection (>680 m/s) together with a newly introduced repetitive regime opens possibilities for usage in needle-free drug administration into materials with elasticity covering the wide spectrum of biological soft tissues like blood vessels, all skin layers, scarred or dried skin or tumors.