Clean the cracked alabaster with a damp microfiber cloth.
Moisten a cotton swab with denatured alcohol and use it to spot clean the crack.
Mix the two parts of the epoxy resin as directed by the manufacturer. If you want to color the epoxy, add a small amount of pigment and stir until it's uniform. Add more pigment as necessary until the epoxy is the desired color.
Apply the epoxy resin to the alabaster crack with a palette knife. Scrape the palette knife over the crack to push the epoxy into the crack and smooth the surface.
Wipe the excess epoxy off with a soft cloth moistened with denatured alcohol. Allow the epoxy to dry overnight or as directed.
Sand the filled crack with medium- then fine-grit sandpaper until it's perfectly smooth
Apply a small amount of stone polish to a polishing pad. Rub the pad in a circular motion over the repaired area of the alabaster by hand or with a rotary tool until the piece looks shiny and uniform.