Precise analytical models of power supply noise induced jitter (PSIJ) at inverter chains are proposed. Based on the piecewise linear approximated I–V curve model, analytical models of local PSIJ transfer functions at local rising and falling edges are derived. The total PSIJ transfer function of an inverter chain output is then estimated by alternately accumulating the local PSIJ transfer function at local rising and falling edges. Based on several assumptions, the full PSIJ transfer function model is significantly simplified, which provides physical insights of PSIJ at inverter chains. Accuracy of the proposed analytical model is successfully validated by SPICE simulations with 130 nm CMOS technology. In addition, properties of the PSIJ transfer function at inverter chains are analyzed based on the proposed model.