Physical human–robot interaction (pHRI) is an essential skill for robots expected to work with humans, such as assistive or rescue robots. However, due to hard safety and compliance constraints, pHRI is still underdeveloped in practice. Tactile sensing is vital for pHRI, as constant occlusions while grasping make it hard to rely on vision or range sensors alone. More specifically, measuring interaction forces in the gripper is crucial to avoid injuries, predict user intention and perform successful collaborative movements. This work exploits the inherent compliance of a gripper with four underactuated fingers which was previously designed by the authors and designed to manipulate human limbs. A new analytical model is proposed to calculate the external interaction forces by combining all finger forces, which are estimated by using the gripper proprioceptive sensor readings uniquely. An experimental evaluation of the method and an example application in a control system with active compliance have been included to evaluate performance. The results prove that the proposed finger arrangement offers good performance at measuring the lateral interaction forces and torque around the gripper’s Z-axis, providing a convenient and efficient way of implementing adaptive and compliant grasping for pHRI applications.