The oscillatory behaviour of solutions of the equation \[ \frac{\partial^ 2u}{\partial t^ 2}+\alpha \frac{\partial^ 4u}{\partial x^ 4}-(\beta -\gamma \int^{L}_{0}(\frac{\partial u(\xi,t)}{\partial \xi})^ 2 d\xi)\frac{\partial^ 2u}{\partial x^ 2}+c(x,t,u)=f(x,t) \] ((x,t)\(\in (0,L)\times (0,\infty))\) is studied. This equation represents the generalization of Woinowsky-Krieger's model of an extensible beam. The cases of both hinged and sliding ends are analysed in detail. Second order ordinary differential inequalities are established and the sufficient conditions for the oscillatory behaviour are proved. The cases of beams with a combination of clamped, hinged and free edges are studied under the assumption \(\beta =\phi =0\).