Purpose – The spindle behavior of machines and systems depends largely on the choice and design quality of the mechanical components used for the displacement between different parts. As far as very high technology is concerned, air bearings are suitable, for instance, for machining a telescope mirror or for systems used in medical applications that require a micro and nanometric resolution in displacement. Therefore, air bearings play a crucial role in ensuring spindle stability in machines and systems. The static and dynamic behavior of air spindles is dependent on several parameters, such as external load, dimensions, supply pressure, manufacturing capability and fluid properties.Design/methodology/approach – This paper presents a methodology for the calculation and analysis of the stability and reliability of machine and system spindles supported by air hemispherical bearings. The static and dynamic characteristics of air spindles are calculated using the finite element method (FEM). The stochastic Response Surface Method (SRSM) is used for the approximation of the performance function, and the reliability is assessed by Monte Carlo Simulation (MCS) and the First Order Reliability Method (FORM). Findings – The static and dynamic characteristics of air spindles are calculated using the finite element method (FEM). Stochastic Response Surface Method (SRSM) is used for the approximation of the performance function, and the reliability is assessed by Monte Carlo Simulation (MCS) and First Order Reliability Method (FORM). Originality/value – The article presents an original approach for the behavior analysis of machines and systems spindles supported by hemispherical fluid bearings. The methodology based on the finite element method and the principle of structural reliability, allows studying the influence of physical and geometrical parameters on the static and dynamic characteristics and the failure probability of a spindle. Thus, the optimum behavior of a spindle can be predicted for different configurations of a bearing design taking into account the reliability evaluation.