The present invention relates to a penetration assistance kit fitted to a bomb, notably an anti-infrastructure bomb. The kit includes launch tubes mechanically secured to the bomb. In each of the launch tubes is positioned a detonating projectile and its propulsive charge. A detonating projectile can be ejected from its tube by initiation of its propulsive charge. A system is provided for controlling the initiation of each propulsive charge prior to impact of the bomb with a target. The invention applies notably to the penetration of very thick walls made of non-metallic material such as concrete, for example. The invention also relates to a penetrating projectile equipped with such a kit and to a method of getting such a projectile to penetrate a target.