Irwin,
Contact is generally a manipulation of a Truss element for which you can designate a stress-strain curve. Basically, you define the stress-strain curve in such a way that it has no modulus of elasticity (i.e. a flat stress-strain curve) until you reach a strain nearly equal to the length of the element. Once you shortened the element to a certain length, the stress-strain curve then indicates a large modulus. If you manually create this elements, be careful that you don't change this stress-strain curve too rapidly or the problem may not converge.
Many FE packages have incorporated this "curve truss" element and predefined the stress-strain curve renaming the element a "contact" element. You generally have to be in a non-linear analysis method to use this feature. I know Algor and NENastran have it. I'm also pretty sure that COSMOS can do it. Not sure about MSC Nastran, but do agree that it is in FEMAP.