The present invention relates to rigid-buckling-resistant-fluted containers with an arcuate outer rim. The container such as a pressformed paperboard plate of overall diameter “D” including a generally planar bottom region, an upwardly extending fluted region surrounding the generally planar bottom region, and an outwardly and downwardly extending peripheral region having an arcuate radial profile. The containers being produced of a lightweight board but exhibiting high strength and rigidity relative to the low weight board.