If you want to stick with BibTeX, I suggest you proceed as follows:
Find the file apalike.bst in your TeX distribution, make a copy of this file, and name the copy (say) apalikeCAPS.tex. (Don't edit an original file of the TEX distribution directly.)
Open the tile apalikeCAPS.bst in a text editor. The program you use to edit your tex files will do fine.
In this file, locate the function called emphasize. (The function starts on line 200 in my copy of the bst file.)
After this function, insert the following code:
FUNCTION {makeuppercase}
{ duplicate$ empty$
{ pop$ "" }
{ "\MakeUppercase{" swap$ * "}" * }
if$
}
As you can probably guess, this function uppercases its argument.
Find the function format.lab.names. (It should start around line 848, allowing for the 5 or 6 new lines you created when you inserted the new function.) In this function, change the line
s #1 "{vv~}{ll}" format.name$
to
s #1 "{vv~}{ll}" format.name$ makeuppercase
In addition, change the line
{ " and " * s #2 "{vv~}{ll}" format.name$ * }
to
{ "--" * s #2 "{vv~}{ll}" format.name$ * makeuppercase }
Note that the second line has undergone two changes: " and " has been replaced with "--" (an "en-dash"), and makeuppercase has been inserted after format.name$ *.
Save the file apalikeCAPS.bst either in the directory that contains your main tex file or in a directory that's searched by BibTeX. If you choose the second option, be sure to also update the filaname database of your TeX distribution.
- In your main tex file, change the directive
\bibliographystyle{apalike} to \bibliographystyle{apalikeCAPS} and do a full recompile (latex-bibtex-latex-latex) to fully propagate all changes.
Happy BibTeXing!
Aside: As @MarcoDaniel has pointed out in a comment, quite a few of natbibs capabilities aren't available if apalike (or apalikeCAPS) is used as the bibliography style. For instance, the package's longnamesfirst option doesn't work, and neither do the "starred" variants (\citet*, \citep*, etc) of the citation-generating macros. (More precisely, \citet* produces the same output as \citet does, etc.)
The output of a full MWE:

\RequirePackage{filecontents}
\begin{filecontents}{mybib.bib}
@misc{uno,
author = "Anna Author",
title = "Thoughts",
year = 3001,
}
@misc{due,
author = "Anne Author and Bertha Buthor",
title = "Further Thoughts",
year = 3002,
}
@misc{tre,
author = "Anne Author and Bertha Buthor and Carla Cuthor",
title = "Final Thoughts",
year = 3003,
}
\end{filecontents}
\documentclass{article}
\usepackage[authoryear]{natbib}
\bibliographystyle{apalikeCAPS}
\begin{document}
\citep{uno}, \citep{due}, \citep{tre}
\bibliography{mybib}
\end{document}
\documentclass{...}and ending with\end{document}. – Marco Daniel Feb 21 '17 at 16:17natbib) or BibLaTeX? In case of BibTeX, whichbibliographystyleand can you use another one? In case of BibLaTeX, did you already redefine anything? Please post a full minimal working example containing all those crucial information. – Manuel Weinkauf Feb 21 '17 at 17:51apalikeas your cite style. This is relevant for the formatting. You could try to find a more suitable style, or try to create one with makebst. But since you are apparently writing a report and are not bound to any particular templates, I would suggest to switch to BibLaTeX. All formatting is much more flexible and on-the-fly in this system. A solution for your particular problem could for instance be found here. – Manuel Weinkauf Feb 21 '17 at 18:41