Large-amplitude extensional standing waves in metals are studied theoretically and experimentally. Starting from the nonlinear elastodynamic equation for perfectly elastic solids, a one-dimensional second-order model is formulated for resonant rods. Losses are neglected and superposition of forward and backward waves is assumed. Spatial distributions of the force and particle velocity are obtained theoretically as well as the waveforms. The experimental work consists of measuring and analyzing the vibration signal along the length of cylindrical rod samples of a titanium alloy at constant temperature. Stepped rod samples are used to achieve higher strain amplitudes. The samples are driven by means of a piezoelectric transducer. The vibration amplitudes and waveforms are monitored by using a nonintrusive laser vibrometer. From a comparison between the experimental and theoretical results a value for the nonlinearity parameter of the titanium alloy is derived.