Why is it that spherical submarines can withstand greater depths than rectangular submarines?

The physics of a spherical object make it able to withstand greater pressures than one of a rectangle.

A sphere under pressure will encounter the same pressure at all sides of the sphere - an object with flat sides and corners (weak spots) will cave under pressure faster as the edges and centers of the flat areas are the weaker areas.

The design concept is actually taken from nature - the common egg. Most people have never really thought about why and eggshell is so strong, but it's due to it's relatively oval shape. This is why modern submarines are made today in either a teardrop or cigar shaped hull design, with flexible alloy steel. Not only does the shape mean it's much stronger at deep depths, the flexible alloy allows the boat to contract and expand with external sea pressure as it rises and dives. Boats with non-flexible hull materials (e.g., Russia and China) have strong hulls, but since they don't flex, they become brittle over time with each dive and surface. Consider the eggshell once again - over time, if you exert pressure on it steadily, it'll crack and then break.