Three-dimensional (3D) bioplotting has been widely used to print hydrogel scaffolds for tissue engineering applications. One issue involved in 3D bioplotting is to achieve the scaffold structure with the desired mechanical properties. To overcome this issue, various numerical methods have been developed to predict the mechanical properties of scaffolds, but limited by the imperfect representation of one key feature of scaffolds fabricated by 3D bioplotting, i.e., the penetration or fusion of strands in one layer into the previous layer. This paper presents our study on the development of a novel numerical model to predict the elastic modulus (one important index of mechanical properties) of 3D bioplotted scaffolds considering the aforementioned strand penetration. For this, the finite element method was used for the model development, while medium-viscosity alginate was selected for scaffold fabrication by the 3D bioplotting technique. The elastic modulus of the bioplotted scaffolds was characterized using mechanical testing and results were compared with those predicted from the developed model, demonstrating a strong congruity between them. Once validated, the developed model was also used to investigate the effect of other geometrical features on the mechanical behavior of bioplotted scaffolds. Our results show that the penetration, pore size, and number of printed layers have significant effects on the elastic modulus of bioplotted scaffolds; and also suggest that the developed model can be used as a powerful tool to modulate the mechanical behavior of bioplotted scaffolds.