Osteochondrosis (OC) is a developmental orthopaedic disease of significant concern in numerous sport horse breeds, with significant international relevance. Using digital radiographs, we assessed the occurrence of hock (tarsocrural joint) OC in 3 048 Pura Raza Española (PRE) horses which took part in a morpho-functional test, in three specific locations in the tarsus limbs: the Distal Intermediate Ridge of the Tibia (DIRT), the lateral trochlear ridges of the talus (LTT), and the medial trochlear ridges of the talus (MTT). An incidence rate of 13.3% was found for hock OC in the analysed sample, with the highest incidence rate observed in DIRT (10.0%) and the lowest in MTT (0.2%). Estimates of genetic predisposition to hock OC were carried out using three genetic approaches: 1a) a binomial threshold model based on the presence or absence of OC, 1b) a multinomial threshold model, on a scale from 0 (absence) to 3 (maximum), and 2) a linear model. The effects considered in the models included sex, genetic origin and stud class. All the analyses were based on the Bayesian inference methodology, using the THRGIBBS3F90 software. The binomial threshold model yielded the most suitable results, with an estimated heritability for Overall hock OC of 0.71 ± 0.055 on the underlying scale (0.53 on the observed scale), ranging in different locations from 0.48 ± 0.087 (LTT) to 0.66 ± 0.063 (DIRT) on the underlying scale (0.10 and 0.38 on the observed scale, respectively). The highest significative genetic correlation was observed between Overall and DIRT (0.97) for approach 1a, and the lowest significant genetic correlation was between Overall and LTT (0.49), for approach 2. This study contributes valuable insights into the genetic predisposition towards, as well as for the potential for selective breeding against, hock OC in PRE horses, and provides a basis for future research and breeding programmes aimed at minimising the occurrence of hock OC and promoting the overall health of this breed.