A phacoemulsification needle having a hollow passageway terminates in a straight needle tip having a rectangular cross-sectional shape larger than the cross-sectional shape of the needle passageway. The tip is 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 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.