Preheat the oven to 350 degrees F (175 degrees C). Grease a 9×13 inch baking pan.
In a large bowl, mix together the vegetable oil and sugar until well blended. Beat in the eggs, one at a time, then stir in the shredded beets and pineapple with juice. Combine the flour, baking powder, baking soda, cinnamon, allspice and salt; stir into the beet mixture until just incorporated. Spread the batter evenly into the prepared pan.
Bake for about 45 minutes in the preheated oven, or until a wooden pick inserted into the center comes out clean. When cool, frost as desired, or eat plain.