Mike,

This is a great way to boil your analysis down to something more manageable.  My approach has been to create a separate analysis in the component file (or subassembly) that you want to replace with springs.  Effectively, you want to run six separate analyses, one for each component of the spring property.  In each analysis:
1) apply a nominal load (or moment) at the interface between the two parts.
2) Determine the linear (or angular) displacement incurred at the interface.   
3) Divide the load by the linear displacement to get lbf/in (or divide the moment by the angular displacement to get in-lbf/radian)

If you need more detail, or want some help on your specific files, don't hesitate to ask.

Good luck
Pete

PS - There's a way to do this with a single analysis: create six unique load sets (one force or moment per load set); DO NOT check the "Sum Load Sets" box in the analysis definition.  In the review of the results, you can apply each load set separately.

Pete,
Thanks for a prompt reply.
I did exactly as you said, but I want to calculate total stiffness, and here I've got a problem.
I've constrained one end of a component and have applied six load cases (three forces and three moments) according CS. From results, I've received six components of displacement (for each load case) which create a symmetric matrix. Solution of such determinant gives six stiffness, and here is the first problem – some of stiffness is negative. What did I miss and how to make it right?
Regards,
Mike