Extending a two-dimensional analytical framework previously developed for understanding contact acoustic nonlinearity (CAN) in a beam-like structure bearing a contact crack, this study reports an analytical model for interpreting CAN induced due to the modulation from a “breathing” crack in a plate-like structure on propagating guided ultrasonic waves (GUWs) in a three-dimensional (3-D) scenario. The “breathing” crack is considered, in a 3-D manner, as a second source to excite additional wave fields. Thorough investigation of the interaction between the probing GUWs and the “breathing” crack leads to explicit, analytical and full-field description of additional wave fields. In this study, influences of reflected and diffracted waves by the crack on the motion of crack surfaces are scrutinized, yielding a depiction of the “breathing” behavior of the crack, beneficial for quantifying the crack-induced source at double frequency, with which the crack-induced nonlinearity (i.e. second harmonic) can be evaluated quantitatively, in conjunction with the use of an elasto-dynamic method. A nonlinearity index is consequently defined to represent the severity of the “breathing” crack. Results obtained from the 3-D model are compared with those from a finite element simulation, to affirm good agreement. This model does not request a benchmarking process against baseline signals for evaluation of damage.