Wash all vegetables under cold water and drain.
Peel the tomatoes by blanching them 30 to 60 seconds in boiling water, then cooling them in cold water so the skins slip off. Core and set aside.
Peel the potatoes and cut into half-inch cubes. Set aside.
Peel the carrots and slice about a quarter-inch thick. Set aside.
Cut the corn from the cob. Set aside.
Slice the celery into one-inch pieces. Set aside.
Peel and chop the onions. Set aside.
Combine all vegetables with the water or broth in a large saucepan, holding back the salt and pepper. Bring to a boil, then reduce to a gentle simmer for 15 minutes.
Season with salt and pepper to taste, if using.
Ladle the hot soup into prepared jars, leaving 1 inch of headspace. Remove air bubbles, wipe the rims, and set lids and bands to fingertip tight.
Load the jars into the pressure canner and add 2 inches of simmering water. Lock the lid, vent steam for 10 minutes, then bring to 10 lbs pressure, adjusting for altitude.
Process pints for 55 minutes or quarts for 85 minutes. Turn off the heat and let the canner return to zero pressure naturally.
Remove the jars and cool undisturbed for 24 hours. Check the seals, label, and store.