5. Cook the roast for 3 to 4 hours or until the meat is fork tender. Use a meat thermometer to determine the roast is done cooking. The internal temperature should reach at least 145 degrees Fahrenheit (63 degrees Celsius).t's an inexpensive cut, with a rich, delicious flavor that makes it a classic main dish for a big home-cooked meal. For tender, pull-apart meat, it should be slow cooked to allow time for the meat to soften and become juicy. Read on to learn how to make a chuck roast. 1  Prep time: 30-45 minutes. 2  Cook time: 3-4 hours.