When that happens you want a tool known as a "Tire Jack."
Chances are, most cyclists have encountered a difficult-to-mount tire at some point or other. It's hard to pinpoint exactly why it happens. Sometimes it's the tire, sometimes it's the rim, and sometimes it's just the wrong combination of tire AND rim. Some brands or models of tires just seem to fit extra tight no matter what rims they're tried on. And one occasionally finds rims that, for whatever reason, will present a problem with any tire (a little larger in diameter than spec?). In any case, a tire jack is the tool that will safely coax those last inches of tire bead over the rim.
I've seen a couple different brands/models of tire jacks out there, but the most common one is sold by Kool-Stop, like this one here:
|Interesting thing - the Kool-Stop name appears nowhere on the tool - but the name "Simson" is molded into the handle. I can only assume that is who actually manufactures the tool for Kool-Stop.|
I've had some frighteningly tight tire/rim combinations, but I've never had a tire that was so tight that I couldn't coax it onto the rim with this tool.
The Kool-Stop is a good tool to keep in the toolbox or workshop. But if you're out on the road and need to change a tire (and you know from experience it's going to be a challenge to mount), then there is a great "mini" version made by VAR that fits in the palm of your hand and can be packed easily in a saddlebag.
|One of the tire levers is stored in the center of the tool. As far as I know, VAR still makes these, but if you find them for sale today, expect the current production ones to be blue, not gray.|