4D printing of shape shifting structures, aka “hinges”, has raised a new standard in many fields. By using these hinges in certain parts of a 3D printed structures, a pre designed complex 3D shape with potential multifunctional application can be achieved from flat structure. This paper proposes a comprehensive semi-empirical model to predict the final shape shifting behavior and magnitude of the hinges printed by FDM process. First, all FDM main parameters are selected and reduced by design of experiment to printing speed, lamina thickness, nozzle temperature as well as printing pattern. In order to develop the model, a time-dependent constitutive model with these four process parameters were extracted for strain of an SMP homogeneous single layer structure using a fractional Zener model accompanied with Multiple Linear Regression (MLR) technique. Thereafter, the mathematical relations for shape shifting behavior of bilayer 4D printed structures were developed for beam bending and twisting by modifying Timoshenko’s constitutive equations. A comprehensive shape-shifting model was established including 3D printing parameters, angles, thickness ratios, activation time and temperature which was compared to the experimental data and results predicted both shape shifting behavior and magnitude of the hinges with good agreement. In addition, a novel flowchart was suggested to design and achieve the desired shape shifting behaviors. The proposed model and flowchart are novel tools to design 4D structures through desired shape-shifting of the hinges.