Abstract: The mat cutting machine includes a base to which is attached, preferably by spring-loaded posts, a trapezoidial-shaped guide bar with a first face oriented to the base at an acute angle, the angle of the beveled cut desired to be made in a mat, and a second face at right angles to this first face. An L-shaped carriage including a cutting blade may be placed on the guide bar by, first, placing one of its edges against the back surface of the guide bar while bringing a portion of the front surface to bear on the front surface of the guide bar, then sliding the remaining portion of the carriage down upon the guide bar while keeping the inner surface of the carriage on the front surface of the guide bar. This action causes the cutting blade to enter a mat at the proper angle. Preferably the carriage and guide bar are made of wood.