A short guide to authentic boxes and chests is available: File:Viking Sea Chests and Boxes A4.pdf.
Information on evidence of chests from Anglo-Saxon England is available thanks to Robert and Hannah Wilkinson.
Design of early medieval boxes and chests
There seems to have been a single design for boxes and chests in the early medieval period.
The accepted design is based on a box made from only 6 pieces of timber, comprising two sides, two ends, a top and a bottom. THE defining method of constructing a period box is that the bottom plate is supported by the ends using central single mortice and tenon joints. The sides are then fixed to the assembled ends and bottom using a half lap joint along the edge, and finally a hinged lid is added. This six board basic design endures well into the middle ages, although later boxes lose the end tenon joint.
The ends are usually sloping inwards to the top, although vertical ends are allowable. The sides are usually vertical but an acceptable variation is to also have these slope in towards the top. Boxes with ends and sides sloping are known as trapezoidal chests. Ends, sides, bottom and lid are always from one single piece of timber ; it is possible to make a chest out of one long plank cutting all the parts from it.
It is in fact the width of available planks that limits the size of period boxes, although back then wider planks would be easier to obtain than they are today. We would struggle to find timber planks wider than around 10 inches unless specially ordered at a saw mill, whereas our counterparts would cut their planks from available trees, so they would pick the tree to use to suit the size of box they wanted.
Lids can be flat or slightly curved, with the curve cut out of a single piece of thicker timber and sometimes hollowed out internally. The lid should slightly overlap the side at the hinge side, and can either overlap other edges or be flush.
The lid is always connected to the rest of the box with simple looped joint metal hinges, usually made from a single iron strap. Leather straps, a continuous single leather flap or loose lids are acceptable within the society but there have not been any boxes found that do not have iron hinges, so to be accurate leather hinges should be replaced as soon as possible, and hingeless boxes provided with some. Modern compound or pinned hinges are not allowed.
Many sea chests within the Society have rope handles to the ends. This is allowed but is in fact not authentic as no sea chests have been found with rope handles. Iron hinged handles are also generally inauthentic. It would seem that very large Viking boxes were designed to be put somewhere to be left there and not frequently moved around.
Unacceptable boxes and chests
Please note that modern square or rectangular boxes (eg blanket boxes) are not authentic and may not be used. These are square sided, made with tongue and grooved planks, or made from laminated boards. Some have posts in the box corners.
Similarly, please note that chests with curved or barrel-top lids (ie 'pirate' chests) are not authentic and may not be used.
Credits: with thanks to Steve Lines.