The purpose of the present paper is development of the Non-singular Method of Fundamental Solutions(NMFS)for 3D isotropic linear elasticity problems.The NMFS is based on the classical Method of Fundamental Solutions(MFS)with regularization of the singularities.This is achieved by replacement of the concentrated point sources by distributed sources over the sphere around the singularity.In case of the displacement boundary conditions,the values of distributed sources are calculated directly and analytically.In case of traction boundary conditions,the respective desingularized values of the derivatives of the fundamental solution in the coordinate directions,as required in the calculations,are calculated indirectly from the considerations of three reference solutions of the linearly varying simple displacement fields.With this,the main drawback of MFS for these types of problems is removed,since the artificial boundary is not present.In order to demonstrate the feasibility and accuracy of the newly developed method,is the NMFS solution compared to the MFS solution and analytical solutions for a spectra of elasticity problems.NMFS turns out to give similar results than the MFS in all spectra of performed tests.The lack of artificial boundary is particularly advantageous for using NMFS in multibody problems.The developments represent a first use of NMFS for three-dimensional solid mechanics problems.