Ultrahigh temperature ceramics (UHTCs) have melting points above 3000°C and outstanding strength at high temperatures, thus making them apposite structural materials for high-temperature applications. Di-borides, nitride, and carbide compounds - processed via various techniques - have been extensively studied and used in the manufacture of UHTCs. Current analytical models, based on our current but incomplete understanding of the theory, are unable to produce a priori predictions of mechanical properties of UHTCs based on their mixture designs and processing parameters. As a result, researchers have to rely on experiments - which are often costly and time-consuming - to understand composition-structure-performance links in UHTCs. This study employs machine learning (ML) models (i.e., random forest and artificial neural network models) to predict Young's modulus, flexural strength, and fracture toughness of UHTCs in relation to a wide range of mixture designs, processing parameters, and testing conditions. Outcomes demonstrate that adequately trained ML models can yield reliable predictions, a priori, of the three aforesaid mechanical properties. The prediction performance on Young's modulus is superior to flexural strength and fracture toughness. Next, the ML model with the best prediction performance is utilized to evaluate and rank the impacts of input variables on Young's modulus. Finally, on the basis of such classification of consequential and inconsequential input variables, this study develops an easy-to-use, closed-form analytical model to predict Young's modulus of UHTCs. Overall, this study highlights the ability of data-driven numerical models to complement, or even replace, time-consuming experiments, thereby accelerating the development of UHTCs.