We present an attempt towards the many-body description of spontaneous fission based on the semiclassical Vlasov equation and the Feynman path integral method. We define suitable collective variables from the Vlasov solution and use the imaginary time technique for the dynamics below the Coulomb barrier. We demonstrate (1) the stability of the Vlasov solution, (2) the ability of this model to calculate the basic features of the whole spontaneous fission process, (3) the sensitivity of the dynamics below the barrier to the mean field potential, and (4) the important role of collective excitations and of particle emission during the fission process. {copyright} {ital 1997} {ital The American Physical Society}