Among various strain gradient theories, the modified couple stress theory, which introduces a single length scale parameter as an additional material property, has garnered significant interest owing to its simplified portrayal of the material behavior. In this study, we investigated whether a single length scale parameter is sufficient to predict the mechanical behavior under two different type of strain gradients: torsion and bending. L-shaped beams made of single crystal copper with thicknesses ranging from 2.4 μm to 9.1 μm were fabricated, and loads were applied using an indenter. The contributions of bending and torsion were controlled by adjusting the loading position. Through these experiments, we demonstrated the existence of elastic size effect of single crystalline materials under strain gradients. Specifically, size effect was observed in both bending and torsion, with a larger effect observed in cases closer to pure bending. Moreover, we report that the modified couple stress theory and the modified strain gradient theory are not applicable for simulating size effect under combined loading. This discovery highlights the necessity for the development of a new theory capable of adequately simulating size effect under the intricate loading scenarios encountered in practical applications.