The invention relates to a method and an apparatus for deep-drawing a tray (1) from fiber-based sheet material (2), such as polymer coated board. The apparatus comprises a female moulding tool (3), which comprises a cavity (7) for forming the tray bottom outwardly, a male moulding tool (4), which comprises a plunger plate (11) for forming the tray bottom inwardly, the plunger plate being movable with respect to the cavity for forming the tray, and clamps (6, 15) with an interface for holding the sheet material and forming a tray rim flange. According to the invention by laterally distancing at least one of the moulding tools (3, 4) from the sheet material leeway is provided for free forming of the tray side walls while wrinkling or tearing of the same is avoided. Spacer plates (13) may be positioned behind the plunger plate (11), to adjust its position in relation to the cavity (7) of the female moulding tool (3). The cavity may have a separate bottom plate (8) and spacer plates (9) there below, or screw means may be provided for adjusting the distance of the bottom of the cavity from the clamp interface and thereby varying the depth of the tray.