The objective of the present study is the numerical investigation of the inertial cavitation threshold in soft tissue under different multi-frequency signals of high intensity focused ultrasound (HIFU). For the modeling of bubble dynamics, the Gilmore-Akulichev-Zener model was used. The inertial cavitation threshold was calculated for different criteria, for different signal modes (single-, dual-, and triple-frequency), and for different viscoelastic mediums. Effect of nonlinear wave propagation and mechanical effects of acoustic caviation have been also studied. The obtaining results demonstrated that a criterion, based on bubble size, gives lower threshold values than a criterion using bubble collapse velocity. An increase in the values of viscosity and elasticity leads to a rise in the threshold amplitude. Analyzing threshold values for dual- and triple-frequency signal modes, it can be seen that the inertial cavitation threshold can be sufficiently reduced when a multi-frequency signal with the correct frequency combination is applied. However, the inertial cavitation threshold also depends on the initial bubble size. This dependency was also investigated in the current study.