Plasmonic nanostructures that support surface plasmon (SP) resonance potentially provide a route for the development of nanoengineered nonlinear optical devices. In this work, second-order nonlinear light scatteringspecifi cally, sum-frequency generation (SFG) and secondharmonic generation (SHG) -from plasmonic nanoantennas is modeled by the Boundary-Element Method (BEM). Far-fi eld scattering patterns are compared with the results calculated by the Mie theory to validate the accuracy of the developed nonlinear solver. The sum-frequency generation from a multi-resonant nanoantenna (MR-NA) and the second-harmonic generation from a particle-in-cavity nanoantenna (PIC-NA) are analyzed by using the developed method. Enhancements of the scattering signals due to double-resonance of the multi-resonant nanoantenna and gap plasmonic mode of the particle-in-cavity nanoantenna are observed. Unidirectional nonlinear radiation for the particle-in-cavity nanoantenna is realized. Moreover, the emission direction of this radiation can be controlled by the location of the nanosphere. This work provides new theoretical tools and design guidelines for plasmonic nonlinear nanoantennas.