A round cutting insert for a milling tool having a center axis and a neutral plane extending perpendicularly thereto. The round cutting insert includes a circumferential side surface surrounding the center axis between upper and lower round main surfaces. An upper cutting edge is formed along the intersection of the upper round main surface and the side surface. A plurality of elongated support grooves are arranged in the side surface. Each elongated support groove has a bottom surface extending in a lengthwise direction with opposite flank surfaces converging toward the bottom surface and extending in parallel with the lengthwise direction of the elongated support groove. The lengthwise direction of each elongated support groove forms an acute angle with the neutral plane as seen in a side view. At least one of the opposite flank surfaces of each elongated support groove is configured as a side support surface.