Abstract: The steady state laminar flow of non-linear viscoelastic fluid with Simplified Phan-Thien Tanner (SPTT) model between two plates with an angle is studied analytically for the case of continuous motion of the lower plate. Linear form of stress coefficient is used in the constitutive equation. For the linear stress coefficient the dimensionless pressure gradient and velocity profile are obtained for a wide range of upper plate slope, Deborah number and elongational parameter. The results indicate the strong effects of the viscoelastic parameters on velocity profile and the dimensionless pressure. While upper plate slope decreases for constant dimensionless viscoelastic group εDe2, maximum pressure reduces and location of maximum shifts to entrance of channel, as limiting case for two parallel plates the dimensionless pressure gradient approaches to zero. Increasing of dimensionless viscoelastic group εDe2 in constant upper plate slope, decreases maximum pressure but mean dimensionless pressure promotes and pressure profile changes to more uniform distribution.