Stimulation of deep brain regions with Transcranial Magnetic Stimulation (TMS) may have an important role as a therapy to treat chemical dependency and depression. The coils traditionally used in TMS, however, have a poor performance in stimulating deep neurons. In this work we study the usage of high permeability cores combined with coils specifically designed to induce fields that decay slowly with depth. By using the finite elements method we show that the use of such cores increases the field's magnitude, decreases its decay rate and improves its focality. Such improvements make these high permeability core coils more suited to stimulate deep brain regions.