In the grasping and manipulation of 3D deformable objects by robotic hands, the physical contact constraints between the fingers and the object have to be considered in order to validate the robustness of the task. Nevertheless, previous works rarely establish contact interaction models based on these constraints that enable the precise control of forces and deformations during the grasping process. This paper considers all steps of the grasping process of deformable objects in order to implement a complete grasp planning pipeline by computing the initial contact points (pregrasp strategy), and later, the contact forces and local deformations of the contact regions while the fingers close over the grasped object (grasp strategy). The deformable object behavior is modeled using a nonlinear isotropic mass-spring system, which is able to produce potential deformation. By combining both models (the contact interaction and the object deformation) in a simulation process, a new grasp planning method is proposed in order to guarantee the stability of the 3D grasped deformable object. Experimental grasping experiments of several 3D deformable objects with a Barrett hand (3-fingered) and a 6-DOF industrial robotic arm are executed. Not only will the final stable grasp configuration of the hand + object system be obtained, but an arm + hand approaching strategy (pregrasp) will also be computed.