Glue all loose threads to the back of the painting with the help of tweezers and painting repair kit glue.
Cut canvas repair strip according to the size of the rip, with 1-inch margin all around. Reline the whole painting with a new canvas backing if there are several rips or a big rip.
Apply glue on the canvas rip with a brush, carefully avoiding any lumps. Press the canvas repair strip over the tear, smoothing it over the rip; let dry.
Touch up the rip, but use color only if you are an artist yourself. Use plain/translucent encaustic medium for encaustic paintings by making a beeswax and Damar mixture. Melt eight parts beeswax in a double boiler, then add one part Damar until it blends with the beeswax. Cool until it hardens.
Check for the exact color match to apply over the tear. Dab some paint color onto blank canvas first and let this paint color dry. The paint color generally becomes lighter or darker after it has dried; match this new dried color to the painting.
Re-varnish the painting.
Re-tighten the canvas by spraying just enough hot water on the back side of the painting to dampen it. Avoid soaking the canvas as water may seep past the primer and further damage the painting.
Place a hard flat surface like a wood plank on the painted side opposite the dent.
Dry the wet canvas with a blow dryer (unpainted side). The canvas shrinks as it dries, but may take several spray-and-blow dry attempts before the right canvas tautness is achieved. Never dry with a flat iron as it may get so hot that it permanently damages the oils in an oil painting.