The cavitation pressure of spherical gas bubbles is correlated to the fluid viscosity in a theoretical investigation of the viscous Rayleigh–Plesset equation. The analysis is complicated by the absence of a first integral for the dissipative system. A qualitative normal form bifurcation analysis about a double‐zero codimension 2 singularity is used to guide a quantitative estimate of the cavitation pressure by numerical and Melnikov perturbation techniques.