Tigran,
You can definitely do what you want. For example, To get the equations of the Oscillator example in WSM, do the following in Mathematica:
Needs["WSMLink`"]
eqns = WSMModelData["Oscillator", "SystemEquations", t];
The equations (25 of them) have many algebraic equations related to the connectivity of the elements (masses, springs,etc.). To get rid of these equations we can get the algebraic variables and eliminate them to simplify the equations:
alg = WSMModelData["Oscillator", "AlgebraicVariables"]
The algebraic variables appear as functions of time in the equations so lets eliminate them by first making a list.
final = Eliminate[eqns, Map[#[t] &, alg]]
final now holds the 4 remaining differential equations.
Regards,
Neil