We investigate a method of selectively targeting cancer cells by means of ultrasound harmonic excitation at their resonance frequency, which we refer to as oncotripsy. The geometric model of the cells takes into account the cytoplasm, nucleus and nucleolus, as well as the plasma membrane and nuclear envelope. Material properties are varied within a pathophysiologically-relevant range. A first modal analysis reveals the existence of a spectral gap between the natural frequencies and, most importantly, resonant growth rates of healthy and cancerous cells. The results of the modal analysis are verified by simulating the fullynonlinear transient response of healthy and cancerous cells at resonance. The fully nonlinear analysis confirms that cancerous cells can be selectively taken to lysis by the application of carefully tuned ultrasound harmonic excitation while simultaneously leaving healthy cells intact.