There is a great number of programming languages and they follow various paradigms such as imperative, functional, or logic programming among the major ones and various methodologies such as structured approach or object-oriented or object-centered approach. A memory management design of a programming language is one of the most important features to help facilitate reliable design. There are two wide-spread approaches in memory management: manual memory management and automatic memory management, known as Garbage Collection (GC for short). Recently, a third approach to memory management called Ownership has emerged. Ownership management is adapted in two recent languages Rust and Swift. Rust follows a deterministic syntax-driven memory management depending on static ownership rules implemented and enforced by the rustc compiler. Though the Rust approach eliminates to a high degree memory problems such as memory leak, dangling pointer and use after free, it has a steep learning costs. Swift also implements ownership concept in Automatic Reference Counting ARC. Though the ownership concept is adapted in Swift, it is not a memory safe language because of possibility of strong reference cycles. In this research, a demonstration of the ownership in Rust and Swift will be discussed and illustrated, followed by analysis of the consequences of memory issues related to each design. The comparison of Rust and Swift is based on ownership, memory safety, usability and programming paradigm in each language. As an illustration, an experiment to compare the elapsed times of two different structures and their algorithms, Binary Tree and Array are presented. The results illustrate and compare the performances of the same programs written in Rust, Swift, C, C++, and Java. / Thesis / Master of Science (MSc)