Using the density functional theory with the plane‐wave ultrasoft pseudopotentials method within the local density approximation (LDA), the magnetic structure of CaRuO3 (hereafter referred to as CRO) is studied as a function of hydrostatic pressure. The calculated results show that: 1) the compressive stress does not cause the disappearance of the ferromagnetic (FM) ground state of cubic CRO but only reduces the magnetic ordering energy and magnetic moment per formula unit, and that 2) the orthorhombic CRO with the Pbnm structure is just in the critical region of the FM, antiferromagnetic (AF), and paramagnetic ground states. Although there is no evidence of an AF phase of CRO at low temperature, the calculated results show that an AF interaction does exist between the Ru atoms of CRO. This can explain the negative Weiss temperature of CRO and the abnormal behavior of the magnetic susceptibility of CRO at low temperature. The AF interaction and the sensitivity to the crystal structure may be the reasons for the various properties of CRO. [ABSTRACT FROM AUTHOR]