An out-of-print pattern for a distinctive muu-muu: "Long or short loose-fitting muu-muu has above elbow length, full raglan sleeves, pockets in side seams and scooped neckline with elastic casing forming self-ruffle that may be worn on or off the shoulders."
This pattern was published in 1980, and copies for sale may be found on the net.
My fabric is a black-background tropical print from Hawaiian Fabric. This dress is easy to make, apart from grappling with the bulk of the fabric when threading elastic through the channel. After several unsuccessful attempts, I found that leaving the elastic about twice as long as the desired finished length made it much easier to thread through and gather, until you are ready to secure and stitch it.
First, however, use a dot of fabric glue to hold the seams near the bias binding channel in place. Then use bias binding wider than specified - 25mm rather than 6mm - and wider elastic as well. I used 12mm non-roll ribbed elastic.
At trying on stage, I found the dress much too long and had to shorten it. Be careful, however, if you do shorten the dress, and do not cut off too much. I prefer to wear the dress on the shoulder rather than off it, and have - eventually, after some trial and error - ended up with a wearable garment.