As some reports suggest, 1.5.1 still suffers from it...

The infamous bouncing bug was mostly fixed in 1.4.1, however, in some odd situations it is reported to appear again. If this happens to you, you're welcome to try this mod.   But surprisingly, there are reports that 1.4.5 has the bug again: Squad Bugtracker Issue #16159, note #19   There's a bug that was seemingly fixed in 1.3 and reintroduced in 1.3.1 - when you enter the scene with some vessels landed they jump up in the air (or in the lack of it). Bug #16159 If you don't experience it, just ignore this post. However, many, including me, do experience it and it is rather frustrating. It is unclear when and how this would be fixed officially, chances are it will only happen in Release 1.4 and this release in my understanding could potentially break many mods, so 1.3.1 might be around for quite a long time. The root reason of this seems to be that the game places the vessels slightly beneath the ground and after that physics kicks in and the ground pushes the vessels outwards with significant force. In many cases, especially on low-gravity worlds this could be disastrous. Usually it looks like this (recording courtesy of Fredrik Wolf)   What does the mod do It intercepts all unpacked (i.e. those affected by physics engine) vessels in the scene right before the physics is about to kick in, determines if they are "submerged" into the ground, raises them slightly above and slowly releases. Now it looks like this: (the recording was done with early version, now the vessels are moved upwards even less)   Features and caveats: Vessels on launch clamps are not affected Kerbals on EVA are not affected by default (configurable) Vessels in Prelaunch state (i.e. just launched from VAB/SPH) are affected by default (configurable) Vessels that are Splashed, Flying, Orbiting, Escaping, or on Sub-orbital trajectory are not affected   Particular vessels can be excluded from stabilization (see config file) If there is a Hangar with attached anchor, it would be reattached after the hangar settled If the vessel is moored to the surface with KAS harpoon, it should be safe If the vessel contains KAS pylons/concrete blocks in attached state (with staticAttached = true, that have physical connection to the ground), they will be reattached like Hangar anchors You might experience some FPS drop during the stabilization, for instance when you are coming into physics range with some other vessel and it goes off-rails.
This usually lasts only about 3 seconds and can be reduced further in config file in exchange for less gentle vessel release.     Compatibility and Robustness This fix has been tested in a bunch of other people's games including mine and so far no issues were reported, but I'm pretty sure something will eventually be blown up - some parts or mods me and all participated in testing don't have weren't tested. Some specific mod may require special treatment. Some particular situations may require special treatment as well. For instance, I'm pretty sure if your base is hanging on a cliff, it would not survive. I just didn't find a cliff in KSP to hang a base on it. BACK UP YOUR SAVE BEFORE TRYING THIS FIX and please report the issue if bad things happen.   Configuration is being done via WorldStabilizer.cfg file inside the mod directory, it should be pretty self-explanatory and there are comments. The mod comes with MiniAVC version checker - obligatory notice:  This mod includes version checking using MiniAVC. If you opt-in, it will use the internet to check whether there is a new version available. Data is only read from the internet and no personal information is sent. For a more comprehensive version checking experience, please download the KSP-AVC Plugin. Licensed under MIT License Kudos to @BahamutoD, @Papa_Joe and all participants of this thread for code pieces I pried into. Thanks for all who participated in testing.   Latest version for KSP 1.3.1 is 0.8.4, for 1.4.3 - 0.9.2, for 1.5.1 - 0.9.3, currently available on GitHub, SpaceDock, CurseForge and CKAN. As there are reports for 1.4.5, proper recompile is expected soon, but other people report 0.9.2 works just fine. Ping me if you badly want 1.4.5 recompile with fixed AVC version. Download from GitHub Download from SpaceDock Download from CurseForge Source code is on GitHub as well. Changelog   Development thread for posterity.