rob1, when you say .375 Winchester Mag you realy mean a .375 Winchester right, not a .375 H&H? There is a big huge difference between a .375 H&H and a .375 Winchester. The H&H has a lot more powder and energy behind the bullet! I have a hard time believing a H&H would not penetrate the bear's skull. But with a .375 Winchester it would not surprize me one bit!