Accurate tissue phantoms are difficult to design due to the complex non-linear viscoelastic properties of real soft tissues. A composite hydrogel, resulting from a mix of poly(vinyl) alcohol and phytagel, is able to reproduce the viscoelastic responses of different soft tissues due to its compositional tunability. The aim of this work is to demonstrate the flexibility of the composite hydrogel in mimicking the interactions between surgical tools and various soft tissues, such as brain, lung and liver. Therefore compressive stiffness, insertion forces and frictional forces were used as matching criteria to determine the hydrogel compositions for each soft tissue. A full map of the behaviour of the synthetic material is provided for these three characteristics and the compositions found to best match the mechanical response of brain, lung and liver are reported. The optimised hydrogel samples are then tested and shown to mimic the behaviour of the three tissues with unprecedented fidelity. The effect of each hydrogel constituent on the compressive stiffness, needle insertion and frictional forces is also detailed in this work to explain their individual contributions and synergistic effects. This study opens important opportunities for the realisation of surgical planning and training devices and tools for in-vitro tissue testing.