A natural stone wall will cost around $8 to $12 per square foot based on the type of stone chosen. A concrete block wall costs $6.10 to $7.60 per linear foot.Homeowners will also need to pay for any other materials needed, including steel bars, sand to keep the stones from rubbing against each other and mortar.ost of Materials. The cost of adding a new wall to a home depends on the material used. Brick walls are often an affordable option, and a hollow brick wall costs around $25.40 per square foot.