How to force two figures to stay on the same page in LaTeX?

I have two images that I want to display on a page as figures. Each eats up little less than half of the space available so there's not much room for any other stuff on that page, but I know there is enough space for both of the figures. I tried to place the figures with [ht] and [hb], both [h] and both [ht] but still I can't get those two images on the same page but instead at least few paragraphs between them.

How do I force those two figures to stay on the same page?

You can put two figures inside one figure environment. For example:

\begin{figure}[p]
\centering
\includegraphics{fig1}
\caption{Caption 1}
\includegraphics{fig2}
\caption{Caption 2}
\end{figure}

Each caption will generate a separate figure number.

If you want to have images about same topic, you ca use subfigure package and construction:

\begin{figure}
 \subfigure[first image]{\includegraphics{image}\label{first}}
 \subfigure[second image]{\includegraphics{image}\label{second}}
 \caption{main caption}\label{main_label}
\end{figure}

If you want to have, for example two, different images next to each other you can use:

\begin{figure}
 \begin{minipage}{.5\textwidth}
  \includegraphics{image}
  \caption{first}
 \end{minipage}
 \begin{minipage}{.5\textwidth}
  \includegraphics{image}
  \caption{second}
 \end{minipage}
\end{figure}

For images in columns you will have [1] [2] [3] [4] in the source, but it will look like

[1] [3]

[2] [4].

I had this problem while trying to mix figures and text. What worked for me was the 'H' option without the '!' option. \begin{figure}[H]
'H' tries to forces the figure to be exactly where you put it in the code. This requires you include \usepackage{float}

The options are explained here

If you want them both on the same page and they'll both take up basically the whole page, then the best idea is to tell LaTeX to put them both on a page of their own!

\begin{figure}[p]

It would probably be against sound typographic principles (e.g., ugly) to have two figures on a page with only a few lines of text above or below them.

By the way, the reason that [!h] works is because it's telling LaTeX to override its usual restrictions on how much space should be devoted to floats on a page with text. As implied above, there's a reason the restrictions are there. Which isn't to say they can be loosened somewhat; see the FAQ on doing that.

Try adding a !, e.g. [h!].