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The hybrid boundary node method (HdBNM) combines a modified function with the moving least squares approximation to form a boundary-only truly meshless method. This paper describes two implementations of the HdBNM, the singular hybrid boundary node method (ShBNM) and the regular hybrid boundary node method (RhBNM). The ShBNM and RhBNM were compared with each other, and the parameters that influence their performance were studied in detail. The convergence rates and their applicability to thin structures were also investigated. The ShBNM and RhBNM are found to be very easy to implement and to efficiently obtain numerical solutions to computational mechanics problems.