  The notion of $\textbf{Gray}$-category, a semi-strict $3$-category in which
the middle four interchange is weakened to an isomorphism, is central in the
study of three-dimensional category theory. In this context it is common
practice to use $2$-dimensional pasting diagrams to express composites of
$2$-cells, however there is no thorough treatment in the literature justifying
this procedure. We fill this gap by providing a formal approach to pasting in
$\textbf{Gray}$-categories and by proving that such composites are uniquely
defined up to a contractible groupoid of choices.
