This paper dealts with the existence of multiple solutions for the two- point boundary value problems of the type \(u''+ f(t, u)= 0\), \(u(0)= 0\), \(u(\pi)= 0\), in terms of the behaviour of the ratio \(f(t, u)/u\) near \(u= 0\) and near infinity. It is assumed that \(f\) is at least a Carathéodory function in \([0, \pi]\times \mathbb{R}\). The authors show that if \(f(t, u)\) grows at most linearly as \(| u|\to \infty\) and is locally Lipschitz, the ``variation index'' yields in quite an elementary way multiplicity result. It appears that the number of solutions depends on the number of Fucik curves that are crossed as \(u\) ranges from 0 to \(\infty\). The paper contains some propositions and theorems for determining the number of solutions. Finally, the authors present two examples in which the method developed can be used to prove the multiplicity in the piecewise linear case.