The leg press lets you load the legs heavily with your back supported. Here is what replaces it, and what each swap asks of you instead.
If you only pick one
The hack squat is the closest thing to a leg press with a different name: back supported, legs loaded, no bar on your spine. No hack squat either? The goblet squat is the one most people can load safely from day one, and it teaches the pattern the front squat needs later.
What it trains
Mainly: The quadriceps, the glutes and, depending on how deep you go and where your feet sit, the hamstrings.
Along with it: The calves get some work at the bottom. The trunk does very little, because the seat carries your upper body.
That supported back is the whole reason people use it: you can load the legs hard without the spine and trunk being the limit. Every alternative below gives some of that back.
Why people look for an alternative
The machine is occupied, or your gym does not have one.
You train at home with free weights only.
You want to keep loading the legs while something else (back, shoulder, wrist) is not up to holding a bar. What is safe for you is a question for a clinician, not for this page.
You want a pattern that carries over to standing more directly.
The alternatives
Hack squat
Covers
The closest match: quads and glutes under load with the back supported.
Leaves out
Another machine, so it does not help if the problem was that you have none.
Kit
A hack squat machine.
Belt squat
Covers
Loads the legs with the weight hanging from the hips, leaving the spine and shoulders out of it.
Leaves out
Needs specific equipment that many gyms do not have.
Kit
A belt squat machine, or a dip belt and a platform.
Goblet squat
Covers
Quads and glutes, easy to learn, easy to load in small steps.
Leaves out
The trunk holds the weight, so it is limited by what you can hold rather than what your legs can push.
Kit
One dumbbell or kettlebell.
Front squat
Covers
Heavily quad-dominant, and it loads far more than a goblet squat can.
Leaves out
Demands wrist, shoulder and trunk positions that take practice.
Kit
A barbell and a rack.
Split squat
Covers
Per-leg loading, so each side does its own work.
Leaves out
Half the total load per rep, and balance is part of the task.
Kit
Bodyweight, dumbbells or a barbell.
Step-up
Covers
Quads and glutes per leg, with a load you can set precisely.
Leaves out
Slower per set, and the step height changes the exercise considerably.
Kit
A box or bench; dumbbells optional.
What this page does not do
What this page does is narrow on purpose. It lists which muscles each option loads with your back supported and which ask your trunk to do the work the seat used to do, and it says what equipment each one takes. It does not tell you how to set the pad, where to put your feet, or whether a back or shoulder that is “not up to holding a bar” should be loaded at all. That last one is a question for a clinician, and a page cannot answer it.
In the app every exercise has a swap button that works the same way: it says which muscles the alternative covers, which it leaves out, and what kit it takes. Filter by what you have and the list is only what you can do.