In order to achieve the mechanical performance of grasping objects with SMA bionic flexible hands, a tendon finite element modeling method is proposed in this article to meet the mechanical requirements of the tendon being subjected to only axial forces and not radial forces. By using finite element dynamic simulation and experimental testing methods, the mechanical characteristics of the SMA bionic hands during the grasping process are analyzed and validated. A finite element dynamic simulation model of the SMA bionic hand grasping process is established to study the overall stress characteristics and contact forces of each phalanx, revealing the grasping characteristics of the bionic hand under SMA driving conditions. By creating a physical prototype of the SMA bionic hand, grasping of different objects is achieved. The results show that the stress in the grasping state of the bionic hand does not exceed 21 MPa, the sum of contact forces is 22 N, the theoretical grasping force is 13 N, and the prototype can grasp objects within a diameter range of 70 mm.