Other research reported that genetic mechanism plays a major role in the development process of biological shapes. The primary goal of this dissertation is to develop novel statistical models to investigate the quantitative relationships between biological shapes and genetic variants. However, these problems can be extremely challenging to traditional statistical models for a number of reasons: 1) the biological phenotypes cannot be effectively represented by single-valued traits, while traditional regression only handles one dependent variable; 2) in real-life genetic data, the number of candidate genes to be investigated is extremely large, and the signal-to-noise ratio of candidate genes is expected to be very high. In order to address these challenges, we propose three statistical models to handle multivariate, functional, and multilevel functional phenotypes, with applications to biological shape data using different shape descriptors. To the best of our knowledge, there is no statistical model developed for multilevel functional phenotypes. Even though multivariate regressions have been well-explored and these approaches can be applied to genetic studies, we show that the model proposed in this dissertation can outperform other alternatives regarding variable selection and prediction through simulation examples and real data examples. Although motivated ultimately by genetic research, the proposed models can be used as general-purpose machine learning algorithms with far-reaching applications.