The current shift of computational research from the software 1.0 (approach of explicitly writing rules and instructions for a computer program) to the software 2.0 (approach of using machine learning algorithms to automatically learn patterns and make decisions based on data) is rapidly changing the landscape of computational mechanics. However, there remains a need for a systematic theory that can interpret the classical numerical methods used in software 1.0 into computational intelligence framework of software 2.0. My proposed theory called Mechanistic Computational Intelligence (MCI) aims to fill the void. The MCI theory is built upon the mathematical basis from Deep Learning Discrete Calculus (DLDC) [1], and scientific and engineering solution principles of Hierarchical Deep Learning Neural Network (HiDeNN) [2]. The DLDC theory interprets deep neural networks combining the kernel theory and classical numerical methods. On the other hand, the HiDeNN classifies and proposes a unified way to solve three general types of problems in science and engineering: type 1 problems where the governing equations are known but there is a need to speed up the computation, type 2 problems for which the knowledge of the governing laws is incomplete, and type 3 problems for which there is no known closed form physical equation.