We use deep V-band surface photometry of five of the brightest elliptical galaxies in the Virgo Cluster to search for diffuse tidal streams, shells, and plumes in their outer halos (r>50kpc). We fit and subtract elliptical isophotal models from the galaxy images to reveal a variety of substructure, with surface brightnesses in the range μV = 26-29magarcsec -2. M49 possesses an extended, interleaved shell system reminiscent of the radial accretion of a satellite companion, while M89's complex system of shells and plumes suggests a more complicated accretion history involving either multiple events or a major merger. M87 has a set of long streamers as might be expected from stripping of low luminosity dwarfs on radial orbits in Virgo. M86 also displays a number of small streams indicative of stripping of dwarf companions, but these comprise much less luminosity than those of M87. Only M84 lacks significant tidal features. We quantify the photometric properties of these structures, and discuss their origins in the context of each galaxy's environment and kinematics within the Virgo Cluster. © 2010. The American Astronomical Society.