The nanoindentation technique is used to analyze the depth dependence of the hardness and the reduced elastic modulus of bulk glasses and glass wool fibers (4-12 mu m in diameter) of calcium aluminosilicate composition. In spite of the fiber geometry and the delicate sample mounting-technique, nanoindentation proves to be a relatively accurate method that provides reproducible data for both hardness (H) and reduced elastic modulus (E-r) of thin glass fibers. It is found that H and E-r are generally lower for the fiber than for the bulk sample. Within a given fiber, both H and E-r are approximately constant with increasing indentation depth. However, both of these parameters decrease with diminishing fiber diameter. This trend is attributed to an increase of the free volume of the fibers with decreasing fiber diameter, i.e. to an increase of the fictive temperature.