Tissue and organ phantoms with realistic anatomical features are becoming increasingly popular in the medical field due to their potential to revolutionize surgical planning and practice. Despite advancements in the production technology using 3D printing and development of materials, the availability of 3D printable materials that accurately replicate human organs’ mechanical properties is limited. Therefore, we developed a family of silicone gel-based inks that can be 3D printed using direct ink writing (DIW) with tuneable viscoelastic properties that mimic a wide range of soft tissues. The control over viscoelastic properties is achieved by fine tuning of silicone formulations with a rheology modifier to promote the encapsulating silicone oil. This strategy not only allows for the recreation of the viscoelastic behaviour profile of a wide range of soft tissues through amplitude and frequency sweeps but also is entirely compatible with DIW printing for medical model manufacturing. Thus, this study stands as one of the few in the literature presenting a DIW printing technology enabling the printing of silicone with such precise control over viscoelastic properties that it allows for different sensations to be experienced by the evaluating medical team.