Characterizing the mechanical properties of engineered tissue constructs provides powerful insight into the function of engineered tissues for their desired application. Current methods of mechanical characterization of soft hydrogels used in tissue engineering are often destructive and ignore the effect of 3D bioprinting on the overall mechanical properties of a whole tissue construct. This work reports on using a non-destructive method of viscoelastic analysis to demonstrate the influence of bioprinting strategy on mechanical properties of hydrogel tissue scaffolds. Structure-function relationships are developed for common 3D bioprinting parameters such as printed fiber size, printed scaffold pattern, and bioink formulation. Further studies include mechanical properties analysis during degradation, real-time monitoring of crosslinking, mechanical characterization of multi-material scaffolds, and monitoring the effect of encapsulated cell growth on the mechanical strength of 3D bioprinted scaffolds. We envision this method of characterization opening a new wave of understanding and strategy in tissue engineering.