  In this note we deal with the problem of determining the essential spectrum
of a Toeplitz operator $T_{f}:A^{2}(\mathbb{D}^{2})\rightarrow
A^{2}(\mathbb{D}^{2})$ acting on the Bergman space $A^{2}(\mathbb{D}^{2})$ of
the bi-disc whose symbol $f\in C(\overline{\mathbb{D}^{2}})$ lies in the space
of continuous functions on the closure $\overline{\mathbb{D}^{2}}$ of the
bi-disc.
