Semiconductor quantum dots are artificial nanoscale systems in which charge carriers, such as electrons, are usually confined in a small two-dimensional (2D) region of space. In many occasions the confinement potential of the electrons is considered to be circularly symmetric with the parabolic form as the most commonly used one. Despite the variety of other confinement potentials with both infinite and finite range, all these choices share the property that the potential is circular in space. While these confinement models can be very good in many circumstances, there are situations in which the experimental setup in a semiconductor quantum dot involves application of several gate potentials which have very sharp geometric features. In these experimental instances, the area depleted of electrons, that represents the confining region is not circular and many times is better approximated as square or rectangular in shape. In this work we introduce a confinement potential that describes the confinement of electrons in a non-circular2D semiconductor quantum dot in which the domain where the electrons are confined has a square or rectangular geometric shape. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.