If you need to submit to SIAM, you should consider using their templates for that. That will probably cause the least hassle for all parties involved. (See also biblatex: submitting to a journal) If you don't write for a SIAM publication, rethink if you really need to use SIAM style or if you can live with a style that looks similar.
AFAIK there is no SIAM style for biblatex, so you will have to roll your own. Start from the standard style that comes closest to what you need. (You can also start from other custom styles, some of them are harder to customise than others, though; the standard styles are always easy to modify.)
That is probably going to be style=numeric. Then start emulating the features you need. A good start is Guidelines for customizing biblatex styles, but you will find help for many more issues on this site.
From the picture I saw, I went with
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[backend=biber, style=numeric, giveninits=true]{biblatex}
\addbibresource{biblatex-examples.bib}
\renewcommand*{\newunitpunct}{\addcomma\space}
\renewcommand*{\mkbibnamefamily}[1]{\textsc{#1}}
\DeclareFieldFormat*{title}{\mkbibemph{#1}}
\DeclareFieldFormat*{citetitle}{\mkbibemph{#1}}
\DeclareFieldFormat{journaltitle}{#1}
\renewbibmacro*{in:}{%
\ifentrytype{article}
{}
{\printtext{\bibstring{in}\intitlepunct}}}
\newbibmacro*{pubinstorg+location+date}[1]{%
\printlist{#1}%
\newunit
\printlist{location}%
\newunit
\usebibmacro{date}%
\newunit}
\renewbibmacro*{publisher+location+date}{\usebibmacro{pubinstorg+location+date}{publisher}}
\renewbibmacro*{institution+location+date}{\usebibmacro{pubinstorg+location+date}{institution}}
\renewbibmacro*{organization+location+date}{\usebibmacro{pubinstorg+location+date}{organization}}
\begin{document}
\cite{knuth:ct:a,sigfridsson,worman,geer,companion,aksin}
\printbibliography
\end{document}

Of course this captures only parts of the style, and only parts of what I could see in the example picture you posted.
biblatexandbiber? Please explain better what the problem is ... – Mensch Sep 19 '16 at 15:22biblatex, they will most likely enforce BibTeX. (Ask them before you get started with anything.) In any way, there probably is no direct SIAM style forbiblatex. So you will have to find a style that is similar. A starting point would be thenumericstyle family. You then modify the styles to your needs. – moewe Sep 19 '16 at 15:35.bibfiles. If that is all you need\bibliography{fileone,filetwo}should work just fine with BIbTeX (incidentally AFAIK that exact line does not work withbiblatex). Or do you mean to do more fancy stuff with that? – moewe Sep 19 '16 at 16:00.bstto remove the fields. But if the the SIAM style prints them, there is a good reason for that: They probably want it that way. The\citetthingy is a different problem though, often numeric styles don't like\citet. But: Do SIAM publications cite like that? Or do they always use the number only? – moewe Sep 19 '16 at 18:49