The top and back of a violin are among the most important components of the instrument, both acoustically and structurally. Centuries ago luthiers identified spruce as the ideal wood of the top and maple as the nearly unanimous choice for the back. This situation holds true today. Why is this so? The answers rests in the mechanical properties of these woods, particularly the properties that characterize the behavior of the top and back in flexural vibration. Five fundamental mechanical properties that hold most of the keys to the acoustical and structural qualities of spruce and maple are (1) density, (2) Young's modulus and (3) damping of waves traveling along the grain, and (4) Young's modulus and (5) damping of waves traveling across the grain. Shear distortion also affects the behavior of the vibrating spruce top and maple back even at low frequencies well within the audio range. Wood selection criteria and the influence of mechanical properties on the quality of the instrument will be discussed.