In the past decade, significant progress has been made in digitizing Sanskrit texts and advancing computational analysis of the language. However, efforts to advance NLP for complex semantic downstream tasks like Semantic Analogy Prediction, Named Entity Recognition, and others remain limited. This gap is mainly due to the absence of a robust, pre-trained Sanskrit model built on large-scale Sanskrit text data since this demands considerable computational resources and data preparation. In this paper, we introduce SansGPT, a generative pre-trained model that has been trained on a large corpus of Sanskrit texts and is designed to facilitate fine-tuning and development for downstream NLP tasks. We aim for this model to serve as a catalyst for advancing NLP research in Sanskrit. Additionally, we developed a custom tokenizer specifically optimized for Sanskrit text, enabling effective tokenization of compound words and making it better suited for generative tasks. Our data collection and cleaning process encompassed a wide array of available Sanskrit literature, ensuring comprehensive representation for training. We further demonstrate the model’s efficacy by fine-tuning it on Semantic Analogy Prediction and Simile Element Extraction, achieving an impressive accuracy of approximately 95.8% and 92.8%, respectively.