This study presents a finite element simulation of elastic waves for detecting anti-symmetric damages in an adhesively-bonded single lap joint. Plane strain elements were used for modeling adherents (aluminum) and adhesives (epoxy). Three types of damage were introduced: thickness reduction, elasticity deterioration, and voids in the adhesive layers, and two excitation and reception arrangements (ER1 and ER2) were used to investigate the detectability of the damage. The simulation showed that symmetrically located damage, such as a thickness reduction, can be detected by one excitation and one reception arrangement (ER1) and anti-symmetric damages, such as elasticity deterioration and voids, can be detected by modified two-point elastic wave excitation (ER2). Compared with the ER1 arrangement, the ER2 arrangement does not require a baseline signal for damage detection; hence, an efficient method of anti-symmetric damage detection in an adhesively-bonded single lap joint is proposed.