Disclosed herein is a delivery catheter for implanting a leadless biostimulator. The delivery catheter includes a shaft and a tubular body having a lumen and an atraumatic end. The atraumatic end includes at least one of a braided, woven or mesh construction configured to facilitate the atraumatic end changing diameter. When a distal portion of the shaft is coupled to a proximal region of the leadless biostimulator, at least one of distally displacing the tubular body relative to the shaft or proximally displacing the shaft relative to the tubular body causes the leadless biostimulator to be received in the volume of the atraumatic end and the atraumatic end to encompass the leadless biostimulator. Conversely, at least one of proximally displacing the tubular body relative to the shaft or distally displacing the shaft relative to the tubular body causes the leadless biostimulator to exit the volume of the atraumatic end.