In the framework of Glauber multiple scattering theory including the three-nucleon force, we can well describe the experimental measurements of deuteron–deuteron elastic scattering differential cross-section at momenta [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] GeV/c and center of mass energies [Formula: see text] and [Formula: see text] GeV. Due to relatively small radius of three-nucleon force it has no effect in the forward direction where [Formula: see text] (GeV/c)2 at any energy. The two-nucleon force is enough to describe the data where the single scattering terms are dominant. At medium energy, the effect of three-nucleon force is clear for [Formula: see text] (GeV/c)2. At the same time, for intersecting storage rings (ISR) energies, the three-nucleon force effect is clearly observed at the minimum of the differential cross-section and for the other values of [Formula: see text] (GeV/c)2 is, in general, small.

In the framework of Glauber optical limit approximation taking into account D-state of deuteron and including three-nucleon force effect, the deuteron–deuteron elastic scattering differential cross-section is calculated at momenta [Formula: see text] [Formula: see text] [Formula: see text][Formula: see text]GeV/c for incident deuteron. The D-state effect is not enough to obtain an agreement with the experimental data. The inclusion of three-nucleon force is necessary to improve the agreement with the data at momentum transferred squared greater than [Formula: see text] (GeV/c)2.