A technique to measure planar elongational viscosity and step-planar stress relaxation, by using a lubricated squeeze flow method with PS and LDPE, has been optimized and established. The effect of experimental conditions, i.e., the viscosity of silicone oil as a lubricant, appeared in the measurement of the planar elongational viscosity. The dependence of the uniform planar deformation behavior on the silicone oil viscosity was greater in LDPE than in PS. A high viscosity silicone oil (3.0×10²Pa-s) was chosen to minimize the loss of lubricant. Although the step-planar stress relaxation experiments required speeds that exceeded the testing machine specification to achieve the step deformation, this problem was successfully solved by inserting a metal spacer between the lower plate and the sample. The high viscosity silicone oil produced uniform deformation in both materials with minimal loss of the lubricant, however, the high viscosity of the silicone oil was believed to lead larger measured G⁰(t) results than the predicted values. The silicone oil viscosity was optimized at a lower value of 1.0×10¹Pa-s which minimized the influence of the silicone oil on the results while still producing substantial lubricity. The measurement of planar elongational viscosity by using this optimal silicone oil showed strain-hardening in both samples, with LDPE showing a stronger dependence. “Time-strain separability” within a certain time period was confirmed for the step planar stress relaxation modulus under the optimized conditions.