Arrays in Unix Bourne Shell

/bin/sh is hardly ever a Bourne shell on any systems nowadays (even Solaris which was one of the last major system to include it has now switched to a POSIX sh for its /bin/sh in Solaris 11). /bin/sh was the Thompson shell in the early 70s. The Bourne shell replaced it in Unix V7 in 1979.

/bin/sh has been the Bourne shell for many years thereafter (or the Almquist shell, a free reimplementation on BSDs).

Nowadays, /bin/sh is more commonly an interpreter or another for the POSIX sh language which is itself based on a subset of the language of ksh88 (and a superset of the Bourne shell language with some incompatibilities).

The Bourne shell or the POSIX sh language specification don't support arrays. Or rather they have only one array: the positional parameters ($1, $2, $@, so one array per function as well).

ksh88 did have arrays which you set with set -A, but that didn't get specified in the POSIX sh as the syntax is awkward and not very usable.

Other shells with array/lists variables include: csh/tcsh, rc, es, bash (which mostly copied the ksh syntax the ksh93 way), yash, zsh, fish each with a different syntax (rc the shell of the once to-be successor of Unix, fish and zsh being the most consistent ones)...

In standard sh (also works in modern versions of the Bourne shell):

set '1st element' 2 3 # setting the array

set -- "$@" more # adding elements to the end of the array

shift 2 # removing elements (here 2) from the beginning of the array

printf '<%s>\n' "$@" # passing all the elements of the $@ array 
                     # as arguments to a command

for i do # looping over the  elements of the $@ array ($1, $2...)
  printf 'Looping over "%s"\n' "$i"
done

printf '%s\n' "$1" # accessing individual element of the array.
                   # up to the 9th only with the Bourne shell though
                   # (only the Bourne shell), and note that you need
                   # the braces (as in "${10}") past the 9th in other
                   # shells (except zsh, when not in sh emulation and
                   # most ash-based shells).

printf '%s\n' "$# elements in the array"

printf '%s\n' "$*" # join the elements of the array with the 
                   # first character (byte in some implementations)
                   # of $IFS (not in the Bourne shell where it's on
                   # space instead regardless of the value of $IFS)

(note that in the Bourne shell and ksh88, $IFS must contain the space character for "$@" to work properly (a bug), and in the Bourne shell, you can't access elements above $9 (${10} won't work, you can still do shift 1; echo "$9" or loop over them)).

As the others have said, the Bourne Shell doesn't have true arrays.

However, depending on what you need to do, delimited strings should suffice:

sentence="I don't need arrays because I can use delimited strings"
for word in $sentence
do
  printf '%s\n' "$word"
done

If the typical delimiters (space, tab, and newline) don't suffice, you can set IFS to whatever delimiter you want before the loop.

And if you need to build the array programmatically, you can just build up a delimited string.

There are no arrays in plain Bourne shell. You can use the following way to create an array and traverse it:

#!/bin/sh
# ARRAY.sh: example usage of arrays in Bourne Shell

array_traverse()
{
    for i in $(seq 1 $2)
    do
    current_value=$1$i
    echo $(eval echo \$$current_value)
    done
    return 1
}

ARRAY_1=one
ARRAY_2=two
ARRAY_3=333
array_traverse ARRAY_ 3

No matter what way to use arrays in sh would you pick it will always be cumbersome. Consider using a different language such as Python or Perl if you can unless you are stuck with a very limited platform or want to learn something.