`Export` to `"VTK"` does not handle `Arrow`, not even `Arrow[Tube[..]]`; but it can handle `Tube` and `Cylinder`: $maxlen = 0.08; $aratio = 4.; tubeArrow[p : {p1_, p2_}, radius_: 0.05] := Module[{len, v, r}, v = p2 - p1; len = 0.5 Norm[v]; len = Min[$maxlen, len]; v = len*Normalize[v]; r = len/$aratio; {Tube[{p1, p2 - v}, 0.5 r], Cone[{p2 - v, p2}, r]} ]; VectorPlot3D[{x, y, z}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}] /. Arrow -> tubeArrow [![enter image description here][1]][1] Export["/tmp/foo.vtk", foo = VectorPlot3D[{x, y, z}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}] /. Arrow -> tubeArrow] (* "/tmp/foo.vtk" *) Import["/tmp/foo.vtk"] [![enter image description here][2]][2] [1]: https://i.sstatic.net/FMxun.png [2]: https://i.sstatic.net/Y8Hbu.png