The aim of this paper is to introduce the concept of generalized biderivations of unital Banach algebras and prove some results concerning generalized biamenability of unital Banach algebras. Let $A$ and $B$ be unital Banach algebras, and let $X$ be a unital $A$- $B$-module. Let $T=Tri(A,X,B)$ be the corresponding triangular Banach algebra. We also study the generalized biamenability of triangular Banach algebras and show that if $X=\{0\}$ and $T$ is generalized biamenable, then $A$ and $B$ are both generalized biamenable.