A phacoemulsification needle having a hollow passageway terminates in a straight needle tip formed off-axis from the passageway, allowing the needle tip to move eccentrically when the needle is subjected to torsional or longitudinal vibratory motion. The tip may be flared or may be coextensive with the needle body. The aspiration passageway formed through the needle body may be formed off-axis from the needle body axis. The tip may also be angled with respect to the needle body. The inner and outer surfaces of the needle tip are roughened, as by sandblasting, to enhance the cutting effect of the tip when used with a non-longitudinal handpiece. The lip of each needle tip is polished to a high degree of smoothness and the edges of the tip are rounded to lessen the incidence of snags or cuts.