Using a food processor or blender, puree the strawberries until smooth. Set aside and do the same thing with the blueberries.
Fill each popsicle mold, starting with the blueberry puree in the bottom. Layer the yogurt and strawberry puree, alternating to create red and white stripes. Push in the popsicle sticks and place the popsicle mold in the freezer. Freeze until firm.
*If you like your popsicles a little rustic, but with straight lines, place the popsicle mold in the freezer after you add each layer. This will allow each layer to harden (so the colors don't mix) and will result in straight red and white stripes.