While language is expressed in multiple modalities, including sign, writing, or whistles, speech is arguably the most common. The human vocal tract is capable of producing the bewildering diversity of the 7000 or so currently spoken languages, but relatively little is known about its genetic bases, especially in what concerns normal variation. Here, we capitalize on five cohorts totaling 632 Dutch twins with structural magnetic resonance imaging (MRI) data. Two raters placed clearly defined (semi)landmarks on each MRI scan, from which we derived 146 measures capturing the dimensions and shape of various vocal tract structures, but also aspects of the head and face. We used Genetic Covariance Structure Modeling to estimate the additive genetic, common environmental or non-additive genetic, and unique environmental components, while controlling for various confounds and for any systematic differences between the two raters. We found high heritability, h2, for aspects of the skull and face, the mandible, the anteroposterior (horizontal) dimension of the vocal tract, and the position of the hyoid bone. These findings extend the existing literature, and open new perspectives for understanding the complex interplay between genetics, environment, and culture that shape our vocal tracts, and which may help explain cross-linguistic differences in phonetics and phonology.