In this study, the production and analysis of a composite vessel were performed. The materials selected for the design of the composite materials were glass fiber/epoxy, carbon fiber/epoxy and Kevlar fiber/epoxy material. Anti-symmetric orientation angles of (30°–30°), (45°–45°), (60°–60°) and (75°–75°) were used for each material. In the design of the vessel, the total thickness of the wall is defined as 3 mm. The containers were modeled using the SOLIDWORKS package program with the wall thickness of 10 and 20 layers. The containers modeled are then analyzed to determine maximum deformation and maximum stress by using the ANSYS WORKBENCH 14.0 package program which analyzes according to the finite element method. While making solutions, a pressure of 1.65 MPa as the test pressure of the vessel was defined as hydrostatic from the inner surface of the vessel, and von-Mises stress and total deformations were determined. As a result of this study, it has been determined that a 60°–60° orientation angle is the most appropriate design angle considering both the deformation values and maximum stress. Maximum stress in the design of composite containers was far below the flow limit and remained within acceptable limits for shape changes.