© 2020 IEEE. In this work, a 3D printed modular soft gripper with highly conformal soft fingers was developed. A soft auxetic structure with compliant ribs is 3D printed simultaneously with each soft pneumatic finger for conformal grasping. The fingers of the soft gripper were printed monolithically, without requiring support material and postprocessing, using a low-cost and open-source fused deposition modeling (FDM) 3D printer that employs a commercially available thermoplastic polyurethane (TPU). The soft fingers of the gripper were optimized using finite element modeling (FEM). The FE simulations accurately predicted the performance of the fingers in terms of deformation and blocked force. Also, FEM was used to predict the behavior of the auxetic structure and its compliant ribs to prove that it highly decreases the contact pressure by increasing the contact area between the soft fingers and the grasped objects. The contact pressure can be decreased by up to 8 times with the implementation of the auxetic structure. Also, the configuration of the highly conformal gripper can be easily modulated by changing the number of fingers attached to its base to tailor it for specific manipulation tasks. A wide variety of objects with different weights, shapes, sizes, textures and stiffnesses can be grasped using the soft modular gripper.