Abstract: The wire is the main processing unit of the low speed wire-cut electrical discharge machine( WEDM-LS). The wire rack is a cantilever structure. Its support member—the up and down wire racks is a cantilever structure. The error of the up and down wire racks is significantly affected by ambient temperature,and the change of the up and down wire racks' relative position makes the wire's position and orientation change directly,which reduce the machining precision. In this paper,the screw theory was used to establish the WEDM- LS' theoretical thermal error model. The finite element method was used to calculate the deformation of the upper and lower wire racks in x,y,and z directions when the ambient temperature changes,and drawn the change of the wire's position and orientation with MATLAB in the Cartesian coordinate system. An experimental platform was built to measure the wire rack's thermal deformation under different ambient temperatures,and establish a thermal error model based on the M-RAN RBF neural network algorithm,which provides a basis for compensating for the numerical control system.Resultsshow that the model residual error is less than 1 μm,and it can well reflect the distribution and the variation of the thermal error.