Apparatus for a jaw assembly for use in a materials testing machine comprising: a jaw housing; a specimen grip assembly situated within the jaw housing and having first and second specimen grips for securely holding an end portion of a test specimen therebetween, the first and second grips respectively having first and second outwardly located surfaces, each of the first and second surfaces being inclined at a first predefined angle; and a jacking mechanism, situated within a recess in the jaw housing, for applying a mechanical force between an interior surface of the jaw housing and a surface of the specimen grip assembly so as to fixedly secure the specimen grip assembly into position within the jaw housing; characterized in that the grip assembly further comprises a grip shell having first and second internal inclined surfaces (413, 417), each of the first and second internal inclined surfaces of the grip shell being inclined at a predefined angle complementary to the first predefined angle at which the first and second surfaces, respectively, of the specimen grips are inclined, the grip shell being positioned around the specimen grips such that the first and second surfaces of the specimen grips abuttingly mate with and slide against the first and second inclined surfaces, respectively, of the grip shell so as to define a wedge-like interface between each specimen grip and the grip shell; wherein the grip shell is a unitary piece of material; wherein the grip shell has a truncated frusto-pyramidal exterior shape with a vertical cross-sectional shape that is trapezoidal; and wherein the grip shell further comprises: first and second external sloping surfaces (403, 405) at opposing ends of the grip shell; and the jaw housing has first and second internal surfaces that are inclined at an angle complementary to the first and second external sloping surfaces, respectively, of the grip shell; the first and second external sloping surfaces of the grip shell abuttingly mating with and sliding against the first and second internal inclined surfaces of the jaw housing such that a separate wedge-shaped interface is formed between the jaw housing and each end of the grip shell. a jaw housing; a specimen grip assembly situated within the jaw housing and having first and second specimen grips for securely holding an end portion of a test specimen therebetween, the first and second grips respectively having first and second outwardly located surfaces, each of the first and second surfaces being inclined at a first predefined angle; and a jacking mechanism, situated within a recess in the jaw housing, for applying a mechanical force between an interior surface of the jaw housing and a surface of the specimen grip assembly so as to fixedly secure the specimen grip assembly into position within the jaw housing; characterized in that the grip assembly further comprises a grip shell having first and second internal inclined surfaces (413, 417), each of the first and second internal inclined surfaces of the grip shell being inclined at a predefined angle complementary to the first predefined angle at which the first and second surfaces, respectively, of the specimen grips are inclined, the grip shell being positioned around the specimen grips such that the first and second surfaces of the specimen grips abuttingly mate with and slide against the first and second inclined surfaces, respectively, of the grip shell so as to define a wedge-like interface between each specimen grip and the grip shell; wherein the grip shell is a unitary piece of material; wherein the grip shell has a truncated frusto-pyramidal exterior shape with a vertical cross-sectional shape that is trapezoidal; and wherein the grip shell further comprises: first and second external sloping surfaces (403, 405) at opposing ends of the grip shell; and the jaw housing has first and second internal surfaces that are inclined at an angle complementary to the first and second external sloping surfaces, respectively, of the grip shell; the first and second external sloping surfaces of the grip shell abuttingly mating with and sliding against the first and second internal inclined surfaces of the jaw housing such that a separate wedge-shaped interface is formed between the jaw housing and each end of the grip shell. first and second external sloping surfaces (403, 405) at opposing ends of the grip shell; and the jaw housing has first and second internal surfaces that are inclined at an angle complementary to the first and second external sloping surfaces, respectively, of the grip shell; the first and second external sloping surfaces of the grip shell abuttingly mating with and sliding against the first and second internal inclined surfaces of the jaw housing such that a separate wedge-shaped interface is formed between the jaw housing and each end of the grip shell.