Yup! I have a Pseudosquilla ciliata, a Gonodactylaceus glabrous and a Gonodactylellus viridis. They are the most amazing animals I have ever kept, full stop.
Depending on the species, you will need a tank of 5 gallons (Small Odontodactylus species, Neogonodactylus wennerae and other inactive, reclusive species that stay under 3 inches), 10gallons for medium sized species like G. glabrous, G. smithii and P. ciliata which are out of their burrows often, 40gallons for a peacock mantis, and 100 gallons for a zebra mantis (L. malculata).
For most species, 3"-5" of aragonite with a layer of crushed coral on top will be fine. The grade of crushed coral depends on the size of the mantis. This rule does not apply to L. malculata and similar species, which can get over 12" and need at least 24" of sand.
You can provide your mantis with a PVC tube which is only slightly larger in diameter than the mantis shrimp and about twice it's body length. It is imperative that you provide it a place to make a burrow, be it PVC tube, holes in live rock or sand to dig in.
You will need a store of live food - crabs, hermit crabs, shrimp and other hard-bodied prey for smashers, damsels, shrimp and other soft-bodied prey for spearers.
Other food that they will take include live, freezedried or frozen brine shrimp, live blackworms or bloodworms (occasionally) and silversides soaked in Selcon (a supplement).