For the structural application of engineering thermoplastics, the knowledge of failure modes depending on their service conditions is essential. The most prevalent failure mode is brittle fracture followed by the slow crack growth (SCG) initiated by surface flaws. In that the general geometry of the surface flaws is semi-elliptical, it is vital to investigate the SCG aspects from such kind of shape. The simple strategy which has been employed to predict the crack growth aspect is an application of conventional law, Paris-Erdogan relationship. The approach is regarded as quite simple since only stress intensity factor (SIF) is needed for a crack driving force term. However, through this empirical relationship, the SCG in engineering thermoplastics cannot be properly modeled. For example, in case of the high-density polyethylene (HDPE), frequently used for water transportation pipelines, the crack usually propagates discontinuously. It arises from the existence of a significant damaged zone in front of the main crack tip, which is normally observed in engineering thermoplastics. Thus, adopting one linear elastic fracture mechanics (LEFM) parameter may not reflect the severe damage zone. To handle this feature properly, a theoretical approach with a reflection of such energy dissipation is necessary. In this study, the crack layer (CL) theory was employed to simulate the discontinuous SCG of semi-elliptical surface crack in HDPE plate with finite thickness. The existing 1-dimensional CL theory was expanded to the semi-elliptical crack growth.