This paper discusses the issues of strength and creep of polymeric materials used in orthodontic appliances. Orthodontic biomechanics is focused on the movement of individual teeth or dental groups as a result of the force applied by orthodontic appliances. Stresses in the construction of functional and biomechanical appliances is generated when using the apparatus in the oral cavity. The orthodontic appliance must maintain its shape and not be damaged during treatment so strength and creep resistance are fundamental properties. It was assumed that the clinical success of orthodontic appliances can be determined by these performance properties. The aim of the work was the experimental assessment of comparative bending strength and creep resistance of selected popular polymer materials used in the production of biomechanical orthodontic appliances. Four commercial materials manufactured by the world class producers were tested: NextDent Ortho Rigid (Vertex-Dental B.V., Soesterberg, The Netherlands) marked as “1A”; Erkocryl (ERKODENT Erich Kopp GmbH, Pfalzgrafenweiler, Germany)-“2A”; Vertex Orthoplast (Vertex Dental B.V.), blue, marked as “3A” and material with the same name as “3A” but orange, marked in the article as “4A”. All the tests were carried out after aging in artificial saliva for 48 h at a temperature of 37 °C. Flexular strength and flexular modulus were made using the three point bending method according to the ISO 178 technical standard. Creep tests were carried out according to the method contained in ISO 899-2. The creep test was carried out in an artificial saliva bath at 37 °C. The creep tests showed significant differences in the strength, modulus and deformability of the tested materials. The strength reliability of the tested materials also varied. The research shows that the 2A material can be used for orthodontic applications in which long-term stresses should be lower than 20 MPa.