Soft continuum robots require differential control of channel pressure across several modules to trace 3D trajectories at the tip. For current designs of such actuators, sheathing is required to prevent radial expansion when the chambers are pressurized. With the recent development of soft materials additive manufacturing, 3D printing has become a promising fabrication method for soft continuum robots. However, most current designs for continuum actuators are based on molding, which are not designed for 3D printing. This paper proposes an internal constraint-based soft continuum actuator for single material 3D printing, with tunable design parameters to render pre-defined motions. The internal constraint method maximizes the superiority of the rapid prototyping solution in terms of customizing the soft continuum actuators with high fabrication speed and design freedom. The internal constraints come in the form of internal beam elements that not only limit the undesired radial expansion (up to ∼14% of conventional design) but also allows the actuator to be pressurized at a higher driving pressure (up to ∼160%) and higher maximum bending angle (up to ∼320%) compared to conventional no-beam design. By tuning the design parameter q (determined by the number of constraint beams n per radial cross-section and the number of such sections k along the axial direction), we can render the actuator to the desired movement under specific driving pressure p. We show numerical simulation and hardware experiment results for a soft actuator to achieve specified bending and twisting motions following this design approach.