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I am working with Digital Elevation Models in format TIFF 2km * 2km. As far as I know DEMs should have a 3d function but in my case the DEMs are flat. They only look 3d because of the hill shading. But when I open the DEM in ArcScene it is flat.

How can I turn the DEM into a real 3d model? How can I see the z values?

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A DEM is simply a grid of values representing elevation. To visualize the elevation in "3D" in ArcScene, right-click the DEM layer and go to properties. Under the Base Heights tab, select the "Floating on a custom surface" radio button, and navigate to your DEM if it is not already populated in the browse box. Hit Apply and OK. ArcScene will render the DEM in 3D.

See the ArcGIS help here.

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In ArcMap use the Identify tool and point at cells (pixels) in the raster. It should give you 2 or more values, among them "Stretched" and "Pixel value". Stretched is the colour/brightness, and changes according to Symbology settings. Pixel value is the raw value, and in the case of a DEM will be your Elevation or Z value.

Use an area well above sea level if possible. If the Z value is in the 0-255 range it's probably colour or brightness value and not elevation at all, and your source image not a DEM.

If the values are in the expected range then Jakub's and Barbarossa's answers apply.

Identify on DEM results with Pixel and Stretched highlighted

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Hillshade raster is a 2D representation of the surface created from the DEM (3D) input. In order to display the hillshade as a "3D" surface, you will need to draped it onto the source DEM (or any other surface that has XYZ values, it could be DEM, TIN, or Terrain) In fact even when you just add a DEM into ArcScene it will initially display flat unless you drape it (float it) on itself. You do that in properties -> Base Heights -> Elevations from surfaces -> Floating on a custom surface

You do the same with any other layer or raster in ArcScene, including the DEM.

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Make sure your coordinate system is projected, not geographic.

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