A human arm is a vital instrument for performing various tasks. To imitate natural design, we developed and characterized a bioinspired modular soft robotic arm fabricated from fabric thermoplastic polyurethane (TPU). The soft robotic arm comprises three link sections, three joints, and an end-effector. Although some soft robotic arms have been designed, they are primarily fabricated with continuous shapes. Therefore, we fabricated a modular and customizable soft robotic arm with different requirements, allowing fast fabrication, prototyping, and assembly, and comprising joint and link sections that can be incorporated together to form an arm with an adjustable number of joints. An analytical approach was used to model the different bending angles at diverse pressures, and a data-driven approach was used to model the angular position with respect to the pressure. Forward and inverse kinematics were performed to calculate the orientation, position, and joint angle of each component. The results showed that the maximum bending angles for each corresponding joint were generally larger for joints number one and three but smaller for joint number two. Moreover, motion analysis data showed that each joint exhibited different bending patterns, and our bio-inspired arm design demonstrated that it could conduct diverse motions at various pressures, in contrast to the soft arms seen in the literature. Additionally, the modular construction of the arm allows it to access larger workplaces, and a gripper should be included in future versions to increase the arm’s capabilities.