Michelin Proteks pop off rims
From your question, I'm getting that the bead of your tire is slipping off the rim. I'm assuming you've looked at the sidewall of the tire and you know the rated pressure but you are not able to pump to max pressure. With skinny road bike rim/tire/tube combos this can get frustrating... Inner tubes can twist or worse get pinched in-between the tire bead and the rim. Pinched inner tubes can hold and blow with a load "crack!" causing violent flats. Or sometimes push the tire bead off as you increase pressure (my assumption for you). Here's my process for installing a tire/tube on a rim:


As always inspect everything. Use your fingertips to inspect inside the tire (don't get cut on the tire bead). I've missed staples and bits of metal here, finger tips are your best friend. Also run your finger on the rim channel where the spokes are. Inspect rim tape, all good? Proceed...
Put enough pressure in the tube to barely have it hold a shape. This is critical as it prevents twisting when installing.
Load the inner tube in the tire. Optional, line the valve up with the tire label or obvious marker, makes it easier to find to fill up with air.
Always start at the valve on the tube, valve hole on the rim. Load the valve into the valve hole.
Hold the wheel in your hands, valve at the top. Push one tire bead on, starting at the valve. Now center up the inner tube check to make sure nothing is twisting. Halfway there.
Again starting at the valve, close up the inner tube in the tire with the other tire bead. Use your thumbs and working from the top 12 o'clock position, slide the tire bead on. Move your hands equally down each side of the wheel attempting to evenly put the tire bead on. It will get tighter as you go and close opposite the valve. This method gives the most slack and helps with that last piece to close up the tire.
With practice you can push all the way on with finger tips. Sometimes I find using the crease where the base of your middle finger and top of palm helps too. If a new tire is too tight, gently use a tire lever under the tire bead to close up the tire. Make sure when using levers you don't pinch inner tube on the rim. If you have to when using a lever slide it a bit along the rim wall to feel for inner tube, if you don't feel metal reposition it.
Last I start at the valve and gently pinch the tire to inspect the outside of the tire bead and the inside of the rim wall. If you have inner tube caught here hold your hands approximately 4 inches apart and gently pinch, pull up and attempt to roll the inner tube inside the tire.
Now fill your inner tube approximately half way. Inspect again, also you can spin the tire slowly to compare the edge of the rim to the tire, check both sides. Do you see any big dips or wobbles? You might need to roll the tire bead up or down on the rim wall to get it to seat correctly.
Last, take your tire to full pressure, install valve cap, you are done.