Combine sugar, cocoa and milk in a medium saucepan. Stir to blend, then bring to a boil, stirring constantly. Reduce heat and simmer. Do not stir again.
Place candy thermometer in pan and cook until temperature reaches 238 degrees F(114 degrees C). If you are not using a thermometer, then cook until a drop of this mixture in a cup of cold water forms a soft ball. Feel the ball with your fingers to make sure it is the right consistency. It should flatten when pressed between your fingers.
Remove from heat. Add butter or margarine and vanilla extract. Beat with a wooden spoon until the fudge loses its sheen. Do not under beat.
Pour into prepared pan and let cool. Cut into about 60 squares.