Thin films fulfil very significant roles in today‘s engineering applications. It is of importance to properly determine the mechanical properties to further utilise thin films in an efficient way. The most widely used tool for characterising thin films is nanoindentation, which is mainly applied to extract the hardness and elastic modulus of thin films on substrates. Since 1992, the standard procedure is the Oliver-Pharr method, which is proven to provide correct results for bulk materials, however, it is not sufficient to be applied for the testing of thin films. Although there is common agreement that mechanical properties can be suitably estimated as long as the penetration stays below 10 % of the film thickness, there are many studies that state the problem of obtaining correct values, even below 10 %. Thus, there is need to investigate this disagreement. This thesis is concentrated on nanoindentation testing of single crystalline (111) Cu films on a single crystalline (0001) sapphire substrate. The material response with respect to tip size, film thickness and indentation load shall be examined. Furthermore, it shall be observed if hardness and elastic modulus provide correct values and if the measured data can be corrected to obtain suitable results. It will be shown that the validity of the 10 % rule of thumb is only appropriate for hardness and elastic modulus cannot be measured for thin films less than 300 nm thick.