One of his more notable pieces is a rosewood sideboard with drawers shaped to avoid the need for handles. The timeless design of the piece combines exotic wood with coloured panels. Another classic is his chaise longue in teak and beech covered in wickered patent leather and produced by Bovirke. Other pieces include tables, desks, sofas and hall furniture, inspired by nature with soft, organic, elegantly curved lines.
From the 1950s, Vodder worked with the furniture company Sibast on several sets of office furniture which did particularly well on the American market, even arousing the interest of Jimmy Carter. In the 1960s, the furniture not only reached the White House but could be seen in banks, airline offices, embassies and hotels across the globe. Vodder also arranged international exhibitions in Sweden, England, Austria and the United States together with Verner Panton and Nanna Ditzel. Vodder worked with a number of manufacturers including Cadovius, Nielaus, Erik Jorgensen, Fritz Hansen, Sibast Mobiler