This paper presents a framework based on multiport network theory for modeling underactuated grippers where the actuators produce finger motion by deforming an elastic transmission mechanism. If the transmission is synthesized from compliant components joined together with series (equal force) or parallel (equal displacement) connections, the resulting multiport immittance (stiffness) matrix for the entire transmission can be used to deduce how the object will behave in the grasp. To illustrate this, a three-fingered gripper is presented in which each finger is driven by one of two linear two-port spring networks. The multiport approach predicts contact force distribution with good fidelity even with asymmetric objects. The parallel-connected configuration exhibited object rotation and was more prone to object ejection than the series-connected case, which balanced the contact forces evenly.