In micro four-point probe measurements, three-way flexible L-shaped cantilever probes show significant advantages over conventional straight cantilever probes. The L-shaped cantilever allows static contact to the sample surface which reduces the frictional wear of the cantilever tips. We analyze the geometrical design space that must be fulfilled for the cantilevers to obtain static contact with the test sample. The design space relates the spring constant tensor of the cantilevers to the minimal value of the static tip-to-sample friction coefficient. Using an approximate model, we provide the analytical calculation of the compliance matrix of the L-shaped cantilever. Compared to results derived from finite element model simulations, the theoretical model provides a good qualitative analysis while deviations for the absolute values are seen. From a statistical analysis, the deviation is small for cantilevers with low effective spring constants, while the deviation is significant for large spring constants where the quasi one-dimensional approximation is no longer valid.