Branched synthetic polyisoprenes are described having a macrostructure and a microstructure very similar to those of natural rubber. According to one aspect, these polyisoprenes have an apparent stress F/S.sub.0 greater than or equal to 0.4 MPa at a relative elongation .alpha. of 150%, applied to a dumbbell-shaped test specimen consisting of the crosslinkable polyisoprene. According to another aspect, these polyisoprenes fulfill the relationship: Cotan .delta..gtoreq.0.3761. .eta..sub.inh+0.15,: (i) where cotan .delta. is the cotangent of the loss angle of a sample of said polyisoprene, measured at 130.degree. C. by means of an instrument known by the trade name "RPA2000", said sample being subjected to shear stress to 10% deformation and at a stress frequency of 0.035 Hz, and where .eta..sub.inh is the inherent viscosity of said polyisoprene, measured in toluene at 25.degree. C. and at a concentration of said polyisoprene in toluene of 0.1 g/dl.