The properties of a one-dimensional (1D) polaron and a bipolaron in the region of strong and intermediate coupling are investigated. The Buimistrov–Pekar (BP) method was chosen for the calculation of the energy of self-trapped states. Calculations were carried out by the variational method using wave functions of various types. The lowest polaron and bipolaron energies were obtained using the Gaussian system of functions. In the limit of weak electron-phonon coupling, both the BP and the Feynman methods lead to a linear dependence of the polaron energy where is the Fröhlich constant of electron-phonon coupling. Such dependence can be interpreted as a transition from an autolocalized (in the strong coupling region) to a delocalized polaron state. At where, and are the high-frequency and static dielectric constants, the critical value of the electron-phonon coupling constant, at which the bipolaron states become unstable, is in the range where the upper limit was calculated with respect to the double energy of the Feynman polaron, and the lower bound was obtained using the Buimistrov–Pekar method. The triplet states of a bipolaron do not form a bound state. The Heisenberg exchange interaction of polarons has an antiferromagnetic character.