A tubular prosthetic semilunar or atrioventricular heart valve is formed by cutting flat, flexible leaflets according to a pattern. The valve is constructed by aligning the side edges of adjacent leaflets so that the leaflet inner faces engage each other, and then suturing the leaflets together with successive stitches along a fold line adjacent the side edges. During operation, when the leaflets open and close, the leaflets fold along the fold line. Distal tabs extend beyond the distal end of each leaflet. The tab portions of adjacent leaflets are folded over each other and sewn together to form commissural attachment tabs. The commissural tabs provide commissural attachment points to accommodate sutures and the like in order to secure the tab to a vessel wall, if a semilunar valve, and papillary muscles and/or chordae tendineae, if an atrioventricular valve.