On of the main problems in the operation of subsea pipelines that convey paraffin oils is the flow startup after long stoppages. Along the path from the reservoir to the platform, the oil experiences significant heat losses, especially to the low-temperature water at the sea bottom. When there is no flow, the oil may reach very low temperatures. Cooling induces wax precipitation and hence gelification of the oil, which may cause blockage of the pipeline. Under these circumstances, pressures much higher than the usual ones may be needed to cause the flow to restart. The knowledge of the minimum pressure level that causes flow after prolonged stoppages is an important piece of information that is needed in the specification of the pipeline pumps. It is known from the literature that the viscoplastic behavior is the main rheological characteristic of gelled oils. In this work we analyzed the flow startup using an ideal viscoplastic material, namely, aqueous Carbopol solutions. These solutions were rheologically characterized, and the measured flow curves were fitted to the Herschel-Bulkley rheological function. Preliminary validation tests unveiled the presence of wall slip at the stainless steel tube wall. For this reason, a different tube was employed, whose material was a polyester resin and whose inner tube wall was roughened. Validation test results for a Newtonian oil were in excellent agreement with the analytical solution (Hagen-Poiseuille). Numerical results were obtained using the viscosity functions determined from the rheological measurements, and confronted with the experimental results for the Carbopol solutions.