Combine flour and shortening in a large mixing bowl. Work the shortening in with a pastry blender or your fingers until completely incorporated.
Dissolve the salt in the water and pour about ⅔ cup of it over the dry ingredients. Immediately work it in with a fork. The dough will be in large clumps. If all the dry ingredients haven't been dampened, add the rest of the liquid.
Scoop the dough onto your work surface and knead until smooth.
Divide the dough into 12 portions and roll each into a ball. Set them on a plate, cover with plastic wrap and let rest at least 30 minutes.
Heat a large skillet or ungreased griddle over medium to medium-high heat.On a lightly floured surface, roll out a portion of the dough into a 7-inch circle. Flatten a ball of dough, flour it, then roll forward and back across it, rotating a sixth of a turn and roll forward and back again. Continue until it is a 7-inch circle. Flour tortilla as needed while rolling.
Lay the tortilla on the hot griddle. After 30-45 seconds, when brown splotches show underneath, flip it over. cook another 30-45 seconds more, until the other side is browned. Do not overcook or the tortilla will become crisp.
Remove and wrap in a clean kitchen towel. Repeat procedure with remaining tortillas and stack them on top of each other.