Locate the cracks between the bricks. Cracks in brick walls are almost always in the mortar joints between the bricks.
Wash excess grime and dirt off the bricks, using a hose or a pressure washer. Allow the bricks to dry.
Remove the cracked mortar between the bricks. Scrape out the inside of the joints with a small chisel or a flat-head screwdriver.
Clean out the joint with a wire brush to remove any small particles, jagged edges and remaining debris.
Fill in the joint cavity with mortar. Apply the mortar with the edge of a putty knife or a masonry trowel. Wipe away excess mortar with a rag, and let it dry.
Clean the area around the crack. Hose off the crack and the surrounding section of wall. Wipe any dirt away from around the crack. Use a cotton-tipped applicator to remove dirt from inside the crack itself. Allow the area to dry.
Load a caulking gun with silicone-based caulk. Make sure the caulk matches or closely resembles the color of your wall so that it blends in well. If you cannot find the right color, use clear silicone caulk.
Insert the nozzle of the caulking tube into the crack. Squeeze the trigger of the caulking gun, and fill the crack until it is level with surface of the wall. Wipe away any excess caulking material with a clean rag. Allow to dry.
Sand the caulk down if it expands too much after it has cured. Use a fine-grit sandpaper.
Put on a pair of safety glasses.
Widen the bottom of the crack, using a hammer and a chisel. Gently tap the bottom of the crack so that the bottom is wider than the top of the crack. This is called undercutting, and it helps to give the concrete epoxy a place in which to expand as it dries. If you fail to undercut the crack, the epoxy can push itself right out of the crack.
Smooth both the inside of the crack and its outer edges with a wire brush. Remove any debris and jagged edges that protrude from inside of the crack. Blow into the crack to help expel any grit left inside.
Fill the crack with concrete epoxy. Allow the epoxy to dry according to the product instructions.
Examine the dried epoxy. See if the epoxy has expanded out of the crack. Sand the epoxy down with fine-grit sandpaper if you need to.