Silicone elastomers are amongst others employed in glass façades as structural connection materials. They are known to be durable adhesives, able to transfer forces under variable loading and atmospheric conditions during their design life. For the dimensioning of adhesive joints, numerical simulations are often used, especially for joints which exhibit large deformations and/or for complex geometries. However, silicones have strong non-linear material behaviour already at small strain deformations, are slightly compressible and show a time-depending behaviour. The current existing material laws do not allow for considering these effects properly in simulation, particularly for combined loading. Therefore a hyperelastic material law for silicones has been developed and validated, based on a strain energy function. For this purpose, test series have been carried out to determine all relevant material parameters needed to describe the strain energy potential, namely tension, compression, shear and multi-axial oedometric test series on non-aged and artificially aged specimens. Furthermore, the softening due to low cyclic loading (Mullins' effect) has been considered and quantified by comparison to quasi-static loading for all test series. The developed hyperelastic model has been implemented into the finite element software Abaqus® for validation and the results of numerical simulations have been compared to experimental results and existing laws. The comparison showed that the proposed model better matched the real behaviour of silicone elastomers and led to an increase in exactness of the numerical simulations of adhesive joints.