Verbal jokes are closely associated with ambiguity, among which lexicogrammatical ambiguity is one of the major mechanisms for the generation of verbally expressed jokes.In systemic functional grammar (SFG), transitivity is analyzed in terms of the realization between meaning and lexicogrammar.This provides an effective way of interpretation for lexicogrammatical ambiguity, which has not been well expounded in the framework of formalist grammar.This paper explores within the SFG theory of transitivity why a joke induced by lexicogrammatical ambiguity is funny and how it is funny, and then a linguistic model is suggested for the analysis of such verbally expressed jokes in English.