Hi Gunter, thanks for posting the file. It seems to be working ok for me over here - what I did was to select your oval solid, then run Transform > Deform > Flow. Then at the first prompt I selected the line, at the second prompt I selected the arc and I get this result here:



That's what you will get initially because it transfers your object by taking the distance of a point as located from the start of the base curve, and moving along the target curve by that same distance, extending off the end by a line if it runs past the end.

You probably want to match things by percentages along each curve rather than just directed distance along each curve. For that enable the "Stretch" checkbox option and then you'll get this result:



Also you'll probably want to shorten your base line so that it does not stick out so far to either side of the object - because the object is only contained within a small area of the line it's also only contained within a small area inside the target curve as well. If you make the line fit the width of your object more closely it will also fit more closely to the extent of the arc as well.

Hope this helps, let me know if you are still stuck.

- Michael