The invention discloses a hydraulic horizontal pushing clamp of a tensile testing machine, which comprises a jaw used for clamping a sample, a clamp body used for supporting the jaw, and oil pressure devices used for promoting the motion of the jaw in opposite directions. The oil pressure devices have two, and are provided at the two sides of the jaw. The invention also provides the tensile testing machine possessing the hydraulic horizontal pushing clamp. The tensile testing machine provided by the invention can completely realize the automatic clamping and loosing the sample, and has the advantages of good pressure maintaining performance and good clamping synchronism.