Cost 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.Hollow bricks feature a unique design with a durable shell and a hollow space in the center of each brick.Traditional brick walls cost around $14.10 per square foot. 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.