The paper introduces a new method called Cartesian Atomic Cluster Expansion (CACE) for machine learning interatomic potentials. CACE is designed to perform all operations in Cartesian coordinates, avoiding the use of spherical harmonics and Clebsch-Gordan contraction, which are common in atomic cluster expansion (ACE) and equivariant message passing frameworks. This approach maintains the rotational symmetry of atomic environments while providing a complete set of polynomially independent features. CACE integrates low-dimensional embeddings of chemical elements, optimized radial channel coupling, and inter-atomic message passing. The resulting potential, named CACE, exhibits good accuracy, stability, and generalizability across various systems, including bulk water, small molecules, and 25-element high-entropy alloys. The paper also discusses the implementation details, benchmark results, and comparisons with other methods, highlighting the advantages of CACE in terms of efficiency, stability, and generalizability.The paper introduces a new method called Cartesian Atomic Cluster Expansion (CACE) for machine learning interatomic potentials. CACE is designed to perform all operations in Cartesian coordinates, avoiding the use of spherical harmonics and Clebsch-Gordan contraction, which are common in atomic cluster expansion (ACE) and equivariant message passing frameworks. This approach maintains the rotational symmetry of atomic environments while providing a complete set of polynomially independent features. CACE integrates low-dimensional embeddings of chemical elements, optimized radial channel coupling, and inter-atomic message passing. The resulting potential, named CACE, exhibits good accuracy, stability, and generalizability across various systems, including bulk water, small molecules, and 25-element high-entropy alloys. The paper also discusses the implementation details, benchmark results, and comparisons with other methods, highlighting the advantages of CACE in terms of efficiency, stability, and generalizability.