It has been found that bent-shaped achiral molecules can form a liquid crystal phase, called the Twist-Bend Nematic (N_TB), which is locally polar and spontaneously twisted having a tilted director, with a conglomerate of degenerate chiral domains with opposite handedness and pitch of a few molecular lengths. Here, using a major extension of the Maier–Saupe molecular field theory, we can describe the transition from the nematic (N) to the N_TB phase. We provide a consistent picture of the structural and elastic properties in the two phases, as a function of the molecular bend angle, and show that on approaching the transition there is a gradual softening of the bend mode in the N phase. This points to the crucial role of the molecular shape for the formation of modulated nematic phases and their behaviour.