Siavash ghorbanian - Department of Mathematics ,Islamic Azad University, Firoozkooh Branch, Firoozkooh, Iran
Hosein ansari - Department of Mathematics,Islamic Azad University,Ahar Branch,Ahar,Iran.

In the paper we consider some free boundary problem of the pseudoparabolic type. We prove the equivalence this problem with the corresponding problem of the variational inequalities (by sufficient smoothness of the solution of the variational inequality), as well as prove existence, uniqueness and smoothness theorems for the weak solution of the variational inequality under some assumptions.