The use of veneer composites as structural components in engineering requires special design. The dimensioning of laminated wood can be optimized by varying the wood species, veneer thickness, orientation, arrangement, number of single layers, and other factors. Composite properties can be calculated using suitable model approaches, such as the classical laminate theory. Thus, an optimization can be achieved. The present study verified the adaptability of the classical laminate theory for veneer composites. Native veneer, adhesive-coated veneer, and solid wood were investigated as raw materials for the plywood layers. Mechanical properties were determined using tensile and shear tests and used as parameters to calculate the composite properties of the plywood. The adhesive coating results in an increase in stiffness and strength compared with the native veneer parameters, which is greater perpendicular to the fiber than in the fiber direction. The increase due to the adhesive decreases with increasing veneer thickness. The plywood was bending tested. The measured Young’s modulus was in the range of 8000–10,700 MPa, the shear modulus was in the range of 500–1100 MPa, and the strength was in the range of 70–100 MPa. The values obtained were compared to the calculations. The best prediction of the plywood properties is obtained by using the properties of the adhesive-coated veneer as a single layer.