Contact state estimation is significant for evaluating grasp stability of bionic hands, especially in unknown environments or without visual/tactile feedback. It still remains challenging, particularly for soft bionic hands without integrating complicated external sensors on soft fingers. Focusing on this issue, a proprioceptive-sensing-based systematic solution is proposed to estimate the contact state of soft bionic fingers in a single grasp. A kinematic model for soft fingers is first developed to capture the joint rotation angles and tendon displacement. A kinetostatic model is further built to estimate the contact force when soft fingers come in contact with objects. On this basis, a system stiffness model for soft fingers during preshaping and initial contact with objects is proposed to perceive the contact state. Moreover, an instantaneous stiffness model for soft fingers when initial contact occurs is developed for estimating the contact position on certain phalanges, especially the contact position along the distal phalange. The proposed proprioceptive-sensing-based approach is the first application in soft fingers without integrating complicated external sensors, which makes them concise and practical. Experiments are carried out to demonstrate the effectiveness and efficiency of our proposal.