As 3D bioprinting continues to evolve as a promising alternative to engineer complex human tissues in-vitro, there is a need to augment bioprinting processes to achieve the requisite cellular and extracellular organizational characteristics found in the original tissues. While the cell distribution within bioinks is typically homogeneous, incorporating appropriate cellular patterning within the bioprinted constructs is an essential first step towards the eventual formation of anisotropically organized tissue matrix essential to its biomechanical form and function. This study describes a new bioprinting technique that uses ultrasonic standing bulk acoustic waves (SBAW) to organize cells into controllable anisotropic patterns within viscous bioinks while maintaining high cell viability. First, we develop a 3D computational model to discern the SBAW pressure pattern in response to multiple ultrasonic frequencies (0.71 – 2 MHz). We then experimentally analyze the patterns and viabilities of human adipose-derived stem cells (hASC) and human osteosarcoma cells (MG63) in alginate as a function of the SBAW frequency. Computational results indicate the formation of parallel pressure strands with higher pressure amplitudes near the bottom of the deposited layer, which is corroborated by experimental images of cell patterning. The inter-strand spacing is found to be affected by the frequency (p < 0.0001), while an interaction effect between the cell type and frequency governs the width of the strands (p = 0.02). Further, we demonstrate the synergistic bioprinting and SBAW-induced patterning of hASC within alginate and gelatin methacrylate (GelMA) constructs in tandem with chemical and photo-crosslinking, respectively. Pertinent cellular patterning and viability of at least 80% were noted in the alginate and GelMA constructs across the experimental design space. Finally, we demonstrate the vat photo-polymerization-based bioprinting of a 3-layered GelMA construct with hASC strand lay pattern of 0-45-90° across the layers. This work represents a step forward in advancing bioprinting capabilities to achieve biomimetic tissue constructs.