The shear traction during frictional sliding depends on the instantaneous sliding strain rate ϵ˙ and on a state variable &psgr; which represents the previous history of the sample. A formulation of rate and state friction covers the continuum between gouge and intact rock, as well as the behavior at high and low normal tractions. A traditional formula for the instantaneous coefficient of friction is retained, μ=μ0+a ln(ϵ˙/ϵ˙0)+b ln(&psgr;/&psgr;0), where μ0 is the steady state coefficient of friction at the reference strain rate ϵ˙0, and a and b are small constants. The normalizing &psgr;0 for isothermal conditions is ΔPN/ΔP0N, where ΔP is the effective normal traction, ΔP0 is a reference normal traction, and N is an exponent. The coefficient of friction of intact rock is approximately μclose-bN ln(ΔP/ΔPclose), where the coefficient of friction is μclose, at the normal traction ΔPclose where essentially all the pore space is closed during steady state sliding. The formulation provides an acceptable fit to the observed coefficient of friction of Westerly Granite at normal tractions up to 1500 MPa including steady sliding and intact rock failure. ¿ 1999 American Geophysical Union