How to convert mesh to a solid model in Solidworks?

If the face count is small enough, Solidworks may be able to import it as a solid or surface. There are also 3rd party programs that can save .stl into some other format that SW can open, none come to mind though. Either way, you'll end up with a model that has tons of 'mesh' faces because it can't re-create the smoothness of the original model the .stl was generated from, so hopefully that's ok.

It's a two years old topic, but I will try to add some info for future reference ...
@FredSWUG pointed very well about the limitation on number of faces.
The best way to do it nowadays would be through plugin. Based on my experience, the best plugin is Power Surfacing.
But if you have only a single or small number parts to be converted, you can try online conversion solution.
There are solutions with instant delivery/conversion, and others that take some hours to send you the file. I found solutions varying from free online conversion to pricey service.
There are prices as low as US$1 per model/conversion.
You may need to do some touch up on the files converted from automated platform before you send it to a CNC or other CAD/CAM machine.
You can check on these platforms:
http://cadmesh.com
https://www.convertcadfiles.com/

Have in mind that, the higher is the model complexity (shape) the harder is to convert the model.
If trying to convert a 3D scanned model, make sure to have a closed mesh and a high-density mesh definition.
Good luck!

File - Open -
Change file type to .stl
Go to options
In STL/VRML menu, change "Import as" to "Solid Body".
As Robert H. says, Solidworks will bring the model in made up of flat faces - I've found that it struggles with large .stl files just due to the face count.

Don't forget that newer versions of SolidWorks have the Scanto3D add-in. This allows the software to deal with mesh models better. The software no longer dies with 10,000 model faces, but I don't know what the new limit is.

I use Design X to "wrap" a surface over the mesh before I import it into SolidWorks. It is not perfect, but it is better than dealing with thousands of model faces. A surface might have only dozens, of faces to deal with. But, their topology is rather random and useless.

Opening a mesh model in SolidWorks is not difficult. Turning a mesh into a parametric model in SolidWorks will require that the model be re-modeled feature by feature. You can use the imported mesh, or surface as a guide to help speed things along, but it is not an easy task.