Recent development in bioprinting technology enables the fabrication of complex, precisely controlled cell-encapsulated tissue constructs. Bioprinted tissue constructs have potential in both therapeutic applications and nontherapeutic applications such as drug discovery and screening, disease modelling and basic biological studies such as in vitro tissue modelling. The mechanical properties of bioprinted in vitro tissue models play an important role in mimicking in vivo the mechanochemical microenvironment. In this study, we have constructed three-dimensional in vitro soft tissue models with varying structure and porosity based on the 3D cell-assembly technique. Gelatin/alginate hybrid materials were used as the matrix material and cells were embedded. The mechanical properties of these models were assessed via compression tests at various culture times, and applicability of three material constitutive models was examined for fitting the experimental data. An assessment of cell bioactivity in these models was also carried out. The results show that the mechanical properties can be improved through structure design, and the compression modulus and strength decrease with respect to time during the first week of culture. In addition, the experimental data fit well with the Ogden model and experiential function. These results provide a foundation to further study the mechanical properties, structural and combined effects in the design and the fabrication of in vitro soft tissue models.