How the shape of asperities affects the wear behavior is still an open question in contact mechanics. This work developed adhesive wear models including the deformable spherical and sinusoidal asperities in contact with a rigid flat by introducing the ductile failure criterion. For spherical asperity, fractures propagating at the corner and then forming spherical-like wear particles are observed under high normal loads, indicating a new Archard-like wear mode. For sinusoidal asperity, it is almost flattened under high normal loads, yielding lamellar wear particles; the wear rate rises first and then decreases as the normal load increases, and both the peak wear rate and the corresponding normal load greatly depend on its shape.