The two flex container properties that affect the position of flex items along the main axis and the cross axis are ‘justify-content’ and ‘align-items’. ‘justify-content’ controls how flex items are distributed horizontally or vertically while ‘align-items’ controls how items are aligned perpendicular to the main axis. For ‘justify-content’ you can use values like ‘flex-start’, ‘center’, and ‘flex-end’. For ‘align-items’ you can use ‘stretch’, ‘center’, and ‘baseline’.