A welding apparatus that includes a first member having a first suture-contacting surface, a second member having a second suture-contacting surface, and a device for moving the first member relative to the second member to define a gap between the respective suture-contacting surfaces. The first member is capable of vibrating and delivering mechanical energy at ultrasonic frequencies. The second member is stationary relative to the first member. A fixture element is adapted to receive and maintain two or more segments of a material to be welded in a predetermined alignment in the gap between the first and second surfaces of the first and second members during a welding operation. According to another aspect of the invention, an ultrasonic welding apparatus includes first and second members with patterned first and second suture-contacting surfaces. The patterned surfaces can be complementary or non-complementary and the surface patterns on each member may vary in either a periodic or a non-periodic manner.