The question is already in the title. I am using "algorithmic" as package and can not find any reference for "FOREACH" definition. I already know that for "algpseudocode" I could use
% define macro foreach
\algnewcommand\algorithmicforeach{\textbf{for each}}
\algdef{S}[FOR]{ForEach}[1]{\algorithmicforeach\ #1\ \algorithmicdo}
But I can not find something similar for "algorithmic".
You can copy the content that is created for \FORALL and replace the necessary elements to create a \FOREACH:
\documentclass{article}
\usepackage{algorithmic}
\makeatletter
% Taken from \FORALL within
% http://mirrors.ctan.org/macros/latex/contrib/algorithms/algorithms.dtx
\newcommand{\algorithmicforeach}{\textbf{for each}}
\newcommand{\FOREACH}[2][default]{%
\ALC@it\algorithmicforeach\ #2\ \algorithmicdo%
\ALC@com{#1}\begin{ALC@for}}
\makeatother
\begin{document}
\begin{algorithmic}[1]
\FORALL{$i$ such that $0 \leq i \leq 10$}
\STATE carry out some processing
\ENDFOR
\FOREACH{$i$ such that $0 \leq i \leq 10$}
\STATE carry out some processing
\ENDFOR
\end{algorithmic}
\end{document}
I did just realize that there seems to be "FORALL" in algorithmic, so one can do:
\begin{algorithmic}[1]
\FORALL{$i$ such that $0\leq i\leq 10$}
\STATE carry out some processing
\ENDFOR
\end{algorithmic}