<p>The parametric vibrations of the flexible beams with account of the geometrically nonlinear deformations and breathing crack are studied. The crack breathing is described by using contact parameter and crack function. The nonlinear integro-differential equation, which describes geometrically nonlinear parametric vibrations of the beams with breathing cracks, is derived from the variational principal of Hu–Washizu. The nonlinear integro-differential equation is transformed into the system of piecewise—nonlinear ordinary differential equations by using the weighted residuals method. Arc length continuation technique and shooting technique are used jointly to study numerically nonlinear oscillations, their stability and bifurcations. The Neimark–Sacker and the saddle-nodes bifurcations are observed due to numerical analysis. Quasi-periodic and chaotic oscillations are studied numerically.</p>