STAAD PRO OR SAP2000 IS USEFUL AND WILL MAKE IT SO EASY FOR U....U CAN CONTACT ME FOR ANY HELP
topgunn77@hotmail.com

The most important part of designing mat foundations is calculating the values for the nodal spring constants (Modulus of Subgrade Reaction MSGR, force/cubic foot typ.)This value can be obtained from a Geotecnical engineer, By the results of plate load tests, by typical published values or by performing load-displacement calculations, given the tributary area and stress for each node. The last method is iterrative and tedious. Pressure/Displacement = MSGR

If you want to design the mat foundation, you need to model the mat with all the nodes as springs. When you say the soil as springs, then the soil springs act in one direction only ( uni direction not bi directional )  

As per DENIRO statment it is deficult to reley on STAAD results. Because in  STAAD or STAAD/Pro there is no option to specify the spring as unidirectional (+Y Dir or -Y Dir). Here this analysis requires many iterations. Kindly checkup with staad capabilities.

But I can advice you to look at STRAP software, where you can specify your spring as uni/bi-directional spring with positive or negative directions.