Detailed computer simulations have been made of the effect of intrinsic noise current on the I-V characteristic and voltage noise spectral density Sv(f) of an ideal Josephson element shunted by a capacitor and resistor. The minimum value of the parameter Βc at which hysteresis appears in the quasistatic I-V characteristic is greater than the noise-free value of ≈1. Moreover, as Βc is increased, a region of large differential resistance Rd appears in the I-V characteristic that is associated with a large increase in SV(0). In this regime the noise current is seen to cause random switching between the superconducting and nonzero voltage states. For all bias conditions, SV(f) > Rd2SI(f) where SI(f) is the spectral density of the intrinsic current noise. A comparison is made between these results and previous calculations. The implications for low-noise superconducting devices are discussed. © 1981 Plenum Publishing Corporation.