Responses elicited by transcranial magnetic stimulation (TMS) over the hand motor area depend on the position and orientation of the stimulating coil. In this work, we computationally investigate the induced electric field for multiple coil orientations and locations in order to determine which parts of the brain are affected and how the sensitivity of motor cortical activation depends on the direction of the electric field. The finite element method is used for calculating the electric field induced by TMS in two individual anatomical models of the head and brain. The orientation of the coil affects both the strength and depth of penetration of the electric field, and the field strongly depends on the direction of the sulcus, where the target neurons are located. The coil position that gives the strongest electric field in the target cortical region may deviate from the closest scalp location by a distance on the order of 1 cm. Together with previous experimental data, the results support the hypothesis that the cortex is most sensitive to fields oriented perpendicular to the cortical layers, while it is relatively insensitive to fields parallel to them. This has important implications for targeting of TMS. To determine the most effective coil position and orientation, it is essential to consider both biological (the direction of the targeted axons) and physical factors (the strength and direction of the electric field).