The rheology of a series of long‐chain randomly branched polybutadienes (PBDs) has been investigated. Branched samples were made through a hydrosilation reaction between a small difunctional crosslinker and the 1,2 groups distributed on the backbone of near‐monodisperse PBD (M w =56 000, 137 000; M w /M n =1.04). The resulting samples have both dispersity in molecular weight and architecture. The species distribution has been studied using size exclusion chromatography and has been found to agree with the Flory–Stockmayer distribution for the random branching of monodisperse chains. Sinusoidal oscillation and creep/creep recovery experiments were done to determine dynamic moduli, zero shear viscosity, and equilibrium creep compliance. The observation that branching is random allows structural parameters to be calculated such as weight fractions and average molecular weights of free chains, arms, and interior chains. These parameters are used in existing rheology models whose results are compared to experimental observation. In particular, qualitative agreement is found for η0 as a function of branching content by applying the model proposed by McLeish and O’Connor [Polymer34, 2998–3003 (1993)] for star/linear blends.