Easily done. Rather than trying to wade through the Help files, this is the old way. I doubt that it has chenged much.

There are two ways to do this:

Click on your Staff Tool and then double-click into the measure to bring up the Measure Attributes Window.

Within the Attributes Window, inside the Items to Display Box, uncheck Time Signatures. You will have to do this for each instrument. This is the Global way to change as it will shut off the time signature display for all measures.

The manual way is to use your Measure Tool, double-click into the measure to bring up the Measure Attributes Window. In the lower left corner of the window choose Time Signature >> Always Hide.

Thanks Mike. Both of those methods sound like they are hiding the time signature rather than eliminating the meter of the music. The thing I want to avoid is having Finale think I'm putting too many or too few notes into a measure. Will hiding the time signature also allow for random numbers of notes/beats per "measure"? And then when I want to have a region (several measures, not a new "movement") of the music metered, will it then move along as usual when I enter notes? What I have in mind is sort of free-flowing notation for a while, then metered (3/4, 4/4, etc.) for a while, and back & forth. 

Fritz Hansen,

You can not “eliminate the meter of the music”.

Each and every measure in Finale must have a meter.

That is just the way Finale works.

But you can choose any meter in any measure - and change to another meter in each and every measure.

And you can hide the meters so that they do not display.

You can also hide barlines.

Basically you can get any layout - metered or un-metered - you can imagine.

Hmm. That doesn't seem very accommodating, but I think I can work within those limitations. Thanks for the info.