Solid-solid interfaces are considered as weak points of the insulation since combination of two solid dielectrics increases the risk of cavities and moisture at the interface against the tangential component of the applied electrical stress. The main objective of this paper is to investigate the impact of the applied contact pressure on shrinkage of the size of cavities on the interface that leads to enhancement in the breakdown strength. Experimental measurements of AC 50 Hz breakdown voltage of solidsolid interfaces assembled under standard laboratory conditions were conducted using two different specimens, namely XLPE and silicon rubber. For the same applied contact pressure, breakdown strength of XLPE-XLPE and silicon rubber-silicon rubber interfaces were also analyzed to yield the influence of elasticity modulus (softness) of the solid material on the effectiveness of the applied pressure. Two different levels of contact pressures were applied for each type of interface and higher interfacial pressure (8.02→11.59 bar) led to improved breakdown strength about 50% for XLPE-XLPE interface whereas the enhancement for the much softer interface (i.e. silicon rubber) was about 7% under increasing pressure (1.34→2.67 bar). Additionally, breakdown strength of silicon rubber interface was found to be higher than that of XLPE interface around 53% at the same applied pressure.