It depends on the verbatim environment in question.
Environment verbatim of package verbatim
If you load package verbatim, then its environment verbatim can be used inside other environment definitions as long it is not hidden inside other groups. Also, it cannot be used as \begin{verbatim}, because verbatim needs to know the name of the parent environment to find the end tag \end{<parent>}. The parent environment name would be overwritten by the LaTeX code for \begin.
Example:
\documentclass{minimal} \usepackage{verbatim} \newenvironment{abc} {\verbatim} {\endverbatim} \begin{document} % This works. \begin{verbatim} abc \end{verbatim} % This does now work. \begin{abc} abc \end{abc} \end{document}

Package fancyvrb
Custom verbatim environments can be created by \DefineVerbatimEnvironment, example from the documentation, slightly modified:
\documentclass{article} \usepackage{fancyvrb} \DefineVerbatimEnvironment{abc}{Verbatim}{% gobble=2, numbers=left, numbersep=2mm, frame=lines, framerule=0.8mm, } \begin{document} \begin{abc} First verbatim line. Second verbatim line. \end{abc} \end{document}

Package listings
Environments can be defined with \lstnewenvironment. Example from the documentation:
\documentclass{article} \usepackage{listings} \lstnewenvironment{pascal}{% \lstset{language=pascal}% }{} \begin{document} \begin{pascal} for i:=maxint to 0 do begin { do nothing } end; \end{pascal} \end{document}

fancyvrbandtcolorboxbefore reinventing the wheel.