It does, but a thick layer of matter is actually a pretty good radiation shield. Material is rated based on its "halving distance" - how many centimeters of stuff it takes for the radiation passing through it to be reduced by half. It never quite blocks all of it, but if you keep piling on additional halvings you can get the radiation levels down as small as you want.

This article has a table of values for how well various types of material blocks gamma rays, for example. Sand has a halving distance of 2.9 inches, and solid stone is 2.2 inches, so a couple of feet thickness will provide thousand-fold reduction in radiation.

Other kinds of radiation penetrate heavy elements better, but those kinds of radiation actually get blocked by light elements instead, such as the hydrogen in water. Mars has a relative abundance of water so you can incorporate that into your shielding too.