The aim of the study was to determine the influence of the wheat bran share, moisture content, barrel temperature and the diameter of the die, in the course of the process along with the possibilities of stabilizing the extrusion-cooking conditions and the physical extrudate properties. Wheat bran in the range from 20% to 80% gives the correct stabilization of extrusion-cooking conditions and obtains a range of varied products with different physical and functional properties. The extrudate including wheat brean in the share from 20% to 50% hard, crispy snacks is used to make useful for direct consumption. An increase of wheat bran in the extruded mixtures leads to a lowering of the radial expansion ratio and an increase in specific density. The products with a higher content of bran (60–80%) have the form of gruels or grits and it are not suitable for direct consumption. It was observed that a higher content of bran decreased the water solubility index of dry mass (WSI) and lowered the water absorption index of the extruded products (WAI). An increase in processing temperatures in the range of 120–220°C contributes to an increase in the radial expansion ratio, a lowering of the extrudate’s specific density, an improvement increase of the WSI and of the WAI. Moisture level (14–29%) generates the product’s structure with only slight expansion and causes changes in the extrudate’s WSI and WAI.