Subsolid pulmonary nodules are commonly encountered in lung cancer screening and clinical routine. Compared to other nodule types, subsolid nodules are associated with a higher malignancy probability for which the size and mass of the nodule and solid core are important indicators. However, reliably measuring these characteristics on computed tomography (CT) can be hampered by the presence of vessels encompassed by the nodule, since vessels have similar CT attenuation as solid cores. This can affect treatment decisions and patient management. We present a method based on voxel classification to automatically identify vessels and solid cores in given subsolid nodules on CT. Three experts validated our method on 170 screen-detected subsolid nodules from the Multicentric Italian Lung Disease trial. The agreement between the proposed method and the observers was substantial for vessel detection and moderate for solid core detection, which was similar to the inter-observer agreement. We found a relatively high variability in the inter-observer agreement and low method-observer agreements for delineating the borders of vessels and solid cores, illustrating the difficulty of this task. However, 92.4% of the proposed vessel and 80.6% of the proposed solid core segmentations were labeled as usable in clinical practice by the majority of experts.