Most cypress shrub roots are not deep, aggressive divers. In ordinary garden soil they spread wide and stay fairly shallow. They fan out near the surface instead of plunging straight down. So the short answer is no for most types you will grow at home.
You can almost watch roots make this choice. They follow water and air, and they grow where those two things sit in the soil. That means your soil type shapes the root system far more than the word cypress on the plant tag ever will. Two plants of the same variety can root in very different shapes depending on the ground you give them.
Give your plant well-drained loam and you get the textbook result. Roots build a broad, fibrous mat that reaches out past the canopy edge to gather water and nutrients. This wide spread is good news for you. It anchors the plant well and keeps roots in the top layers of soil where oxygen is easy to reach.
Heavy or wet ground changes the story. Plant in compacted clay or soggy soil and your roots stay near the surface, because the deeper layers hold too much water and too little air. The plant adapts to what it finds. This is why depth depends on your conditions, not on the name on the tag.
Bald cypress is the one real exception, and it earns its own paragraph. It evolved for swamps and wet riverbanks, so its roots handle standing water that would drown other types. Near water it can push up woody knees, the strange knobby growths that rise from the roots around the trunk. Treat it as a wetland specialist, not a typical shrub, and you will use it in the right spot.
Because cypress shrub roots spread wide, planting technique matters more than digging deep. Dig the planting hole two to three times the width of the root ball but only as deep as the root ball is tall. A wide, shallow hole loosens the soil exactly where the young roots want to travel and helps them establish fast in their first season.
Knowing where to plant cypress comes down to two things: room and drainage. A wide root mat does not crack foundations the way some willows or poplars can, but it still needs space to grow without fighting paving or pipes. Keep the trunk back from hard surfaces so roots are not forced under a path or driveway.
For most dwarf false cypress, roots are not a foundation threat at all. You can plant these compact shrubs in a border or near your patio with no worry. They stay small and their roots stay polite, so they suit tight spaces and mixed beds. If your yard is small, these are your safest pick.
Larger types need more thought. Give a Leyland cypress plenty of room, since a fast-growing hedge that big builds a wide root mat to match its height. Avoid setting any cypress in a low, soggy spot where water pools after rain. You will get weak roots and a stressed plant in that kind of ground.
Save your wettest, worst-draining corner for bald cypress. Its roots tolerate the standing water that kills other species. So the spot nothing else wants becomes the one place this tree thrives. If you match each cypress to your soil this way, you get a strong root system and a plant that stays put for decades.
Read the full article: Cypress Shrub Guide: Best Types and Care