Ordered metallic nanoprism arrays have been proposed as novel and versatile systems for the observation of nonlinear effects such as nonlinear absorption. The study of the effect of the local field reinforcement on the fast optical third order nonlinear response around the Surface Plasmon Resonance is of great interest for many plasmonic applications. In this work, silver nanoprism arrays have been synthesized by the nanosphere lithography method. A low repetition rate tunable picosecond laser source was used to study the irradiance and wavelength dependence of the nonlinear absorption properties around the dipolar and quadrupolar resonances of the nanoarray with the use of the z-scan technique. The irradiance dependence of the on-resonance nonlinearity was studied, and a spectral region where nonlinear absorption is negligible was identified. This is important for the possible application of these materials in optical information processing devices.