In the field of satellite communications, space phased array antennas are integral due to their multi-band and multi-angle communication capabilities. However, the conventional crate structure of these antennas presents a significant drawback in terms of weight, leading to increased launch costs. To address this issue, this paper proposes an innovative design for flexible thin-film carrier phased array antennas, which aims to reduce the transmitting mass while overcoming the challenge of buckling inherent in ultrathin flexible structures. The proposed design incorporates a zero Poisson’s ratio orthogonal elliptic hole structure, which is shown to effectively suppress film wrinkling without compromising the film-carrying capacity. Wrinkling in such structures can detrimentally impact the planarity and, consequently, the electrical performance of the antenna. The paper provides an in-depth exploration of the principle of zero Poisson’s ratio in the context of wrinkle suppression and introduces a novel design concept that involves the strategic placement of orthogonal elliptical holes on the membrane surface of the antenna. Additionally, the paper outlines the design space in which the parameters of these holes influence the wrinkle suppression function, taking into consideration the structural characteristics of the repeating unit of the phased array antenna. This innovative design approach offers a promising solution for reducing the transmitting mass of space phased array antennas while maintaining their planarity and electrical performance, thereby advancing antenna technology for satellite communications.