We established that the contact resistance to the two‐dimensional electron gas (2DEG) in selectively dopedn‐AlGaAs/GaAs heterostructure is crystal orientation dependent. The contact resistance in the [011] direction is the lowest and that in the [01¯1] direction is the highest. The contact resistance monotonically changes between the [011] and [01¯1] directions. We also find the sheet resistance dependence of the contact resistance.