A programmable resistor memory, such as a phase change memory, with a memory element comprising narrow vertical side wall active pins is described. The side wall active pins comprise a programmable resistive material, such as a phase change material. In a first aspect of the invention, a method of forming a memory cell is described which comprises forming a stack comprising a first electrode having a principal surface with a perimeter, an insulating layer overlying a portion of the principal surface of the first electrode, and a second electrode vertically separated from the first electrode and overlying the insulating layer. Side walls on the insulating layer and on the second electrode are positioned over the principle surface of the first electrode with a lateral offset from the perimeter of the first electrode.