One of the biggest surprises in the development of samadhi (concentration) is the insight that samadhi arises from letting go.  Letting go gives rise to relaxation.  Relaxation gives rise to calmness (of mind).  Calmness gives rise to (mental) stability.  And stability gives rise to samadhi.  So, ultimately, deep concentration doesn’t come from holding the mind down with great effort, but from letting it go.  Like many things in Buddhism, this insight is initially very counter-intuitive, but once you understand it, it leads you to discovering new exciting possibilities within your mind.

One week ago, I led a short guided meditation on exploring this relationship between relaxation and concentration.  The participants (all seasoned meditators) found it very helpful, so I decided to share it with you here.  Posted below is the script I wrote and used for the guided meditation.  I hope it’s useful for you as reading material as well.
=== SCRIPT ===
We will now explore the relationship between relaxation and samadhi.  We will first rest our minds in a state of alert relaxation, and once our minds are sufficiently at rest, we’ll invite the arising of samadhi, and see how that works out.
Let us begin by sitting comfortably.  Sit in a position that enables you to be both relaxed and alert at the same time, whatever that means to you.
Let us now take 3 slow, deep breaths.  Taking deep breaths injects both energy and relaxation, so it is always good to start meditations with a few deep breaths.
Now, let us breath normally, and rest our mind by bringing gentle attention onto the breath.  If you like, you can visualize resting the mind on the breath.  Allow the breath to be a resting place, an abode, or a cushion, or a mattress, and let the mind rest on it, very gently.
Let us give our minds a few minutes of relaxation.
(Long pause)
Now, let us see if we can arise samadhi in our minds.  The way to do that is NOT to force the mind into samadhi.  Instead, we do it with an invitation.  We gently invite the mind to transform  relaxation into concentration, if it wants to.  If it doesn’t want to, that’s ok too.  This invitation is given in the spirit of kindness and generosity, to be accepted or declined at will.  Either way, it is fine.
Let us now give our minds a very kind and gentle invitation to give rise to samadhi from calmness and relaxation, if it wants to.  If it doesn’t want to, it’s fine too.  This is just an invitation.
(Medium pause)
If, instead of samadhi, creativity and energy arises in your mind, that is ok too.  Let us allow this energy to be, and allow it to nourish us in any way that it wants.  Just rest our attention gently on the breath while we allow it to happen.
(Short pause)
If, instead, tension and difficulty arise in your mind, that’s ok too.  Just allow it to be, and bring Mindfulness and Compassion to it.  Our responsibility for this sitting is not to control our minds, our responsibility is to generate Mindfulness and Compassion.  Just rest our attention gently on the breath, and continue to give our minds a generous offering of Mindfulness and Compassion, whatever state it wants to be in.
(Long pause)
As we approach the end of this sitting, let us bring our attention back to the present, resting our minds gently on the breath, and becoming aware of all thoughts and sensations as they arise.
(Short pause)
Let me invite you, if you want, to close this session with a dedication.
I aspire to dedicate all my efforts today to the peace, happiness and enlightenment of all sentient beings.
Countless are all sentient beings, I aspire to love them all.
(Short pause, ring bell to end session)