This paper presents a novel, meshfree-based micromechanical model for homogenising the elastic properties and analysing the deformation and microscopic strains/stresses of twill woven composites. The proposed model was based on a minimum unit cell (mUC) whose internal features such as the cross-sectional shape and waviness of yarns were described by using sophisticated functions. The boundary conditions imposed on the mUC were derived by applying an equivalence approach, which converts the standard form of periodic boundary conditions into a generic set of fixed and relative displacement constraints. Theoretical formulations were developed to implement the micromechanical model within the framework of the moving kriging (MK)-based element-free Galerkin (EFG) method. An in-house computer program implementing the proposed model was developed for analysing a typical twill woven composite. Good agreements were found between the meshfree-based predictions and the reference results, highlighting the proposed model capable of homogenising twill woven composites and meanwhile avoiding the commonly required pre-processing tasks such as building an explicit geometry model and generating identical meshes on the mapping surfaces to enforce boundary conditions. Three case studies were also performed to identify the sensitivities of the predicted results to three numerical parameters, i.e. the total number of field nodes, the total number of background cells, and the support domain scaling factor. The results of these studies suggest that the numbers of field nodes and background cells used must be sufficiently large, while the support domain scaling factor in an appropriate range (e.g. 2.0−3.25) to achieve convergent results.