An angled tissue cutting instrument comprises an angled outer tubular member rotatably receiving a flexible inner tubular member. The inner member has a flexible region in correspondence with an angle of the outer member. The flexible region comprises a helically cut length portion of an elongate tubular body of the inner member and a continuous solid flexible surface secured to an outer surface of the body along the helically cut length portion. A method of fabricating a flexible inner tubular member involves forming a helical cut through the solid wall of a length portion of a tubular body and securing a continuous solid flexible surface to the outer surface of the body along the helically cut length portion to form a flexible region.