Hydrogels are widely being used in cell-culture to provide a scaffolding medium, allowing cells to grow in a 3D environment. Typically, 3D-printing is used to layer the different cell-types and to produce structures such as perfusions that lead to miniaturised models of human organs, e.g. lungs, livers, intestines. The application has a fundamentally mechanical nature since: a) printing through a small nozzle induces viscous forces and can kill the cells prematurely; b) viscosity allows better control of the structure geometry and the structures themselves can be subjected to internal pressure loading; and c) the viscoelastic properties of the hydrogel are known to determine cell survival rate in the culture and the establishment of a functioning extracellular matrix. % Experimental observations: Elastic, Dissipative and Stress-Relaxing Cyclically-loaded samples of alginate-gelatine hydrogels under indentation show that the material responds viscoelastically, including relaxation and internal friction, similar to many polymers. The material is very compliant and undergoes large deformations at even very moderate loads. Presented is a homogeneous, objective, finite-strain material model inspired by the microstructure, as observed under electron microscope. The contact problem of the indentation ball is solved by the recently-published Latent Variable Proximal Point algorithm. Finite element discretisation using the FEniCS library allows the model to be parameterised to reproduce the experimentally-observed material responses.