The amsplain bibliography style, as the name suggests, is very similar to the plain BibTeX style and suitable to AMS publications. We just need to use plain instead of amsplain. :)
\begin{filecontents*}{mybibfile.bib}
@book{Knuth:2005:ACP:1036677,
author = {Knuth, Donald E.},
title = {The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions},
year = {2005},
isbn = {0201853949},
publisher = {Addison-Wesley Professional},
}
@book{Knuth:1998:ACP:280635,
author = {Knuth, Donald E.},
title = {The art of computer programming, volume 3: (2nd ed.) sorting and searching},
year = {1998},
isbn = {0-201-89685-0},
publisher = {Addison Wesley Longman Publishing Co., Inc.},
address = {Redwood City, CA, USA},
}
\end{filecontents*}
\documentclass{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\makeatletter
\renewcommand\@biblabel[1]{#1.}
\makeatother
\begin{document}
\nocite{*}
\bibliographystyle{plain}
\bibliography{mybibfile}
\end{document}
With amsplain:

And with plain:

I had to do this dirty trick:
\makeatletter
\renewcommand\@biblabel[1]{#1.}
\makeatother
otherwise, our output would have [1] instead of 1.:

Hope it helps. :)