Finned heat sinks are used to cool power electronics components. We present optimization results for single rectangular, triangular, and trapezoidal fins. After that, we minimize the mass of an existing heat sink consisting of a base plate and a fin array by optimizing the geometrical variables and component locations on the base plate. An analytical solution is used with rectangular fins and a numerical model with trapezoidal fins. Whereas the triangle is the best shape for single fins, in a heat sink flow velocity coupled with geometry favors trapezoids over triangles and rectangles.