Double stranded DNA chain is known to have non-trivial elasticity. We study the effect of this elasticity on the denaturation profile of DNA oligomer by constraining one base pair at one end of the oligomer to remain in unstretched (or intact) state. The effect of this constraint on the denaturation profile of the oligomer has been calculated using the Peyrard-Bishop Hamiltonian. The denaturation profile is found to be very different from the free (i.e. without the constraint) oligomer. We have also examined how this constraint affects the denaturation profile of the oligomer having a segment of defect sites located at different parts of the chain.