The Immersed Finite Element Method (IFEM) is a mathematical formulation for fluid-structure interaction problem like the Immersed Boundary method; in IFEM the immersed structure has the same space dimension of the fluid domain. We present a stability of IFEM for a scheme where the Dirac delta distribution is treated variationally, as in \cite{IBBoffiGastaldiHeltai}; moreover the finite element space related to the structure displacement consists of piecewise continuous Lagrangian elements, at least quadratic. The analysis is performed on two different time-stepping scheme. We demonstrate also that when the structure density is smaller than the fluid one, the stability is assured only if the time step size is bounded from below.